library(tidyverse)

We have 6 Bayesian Bradley-Terry models, Glicko-2, and a “null” ranking model for a total of 8 models to compare.

First we load the relevant tennis match data:

# Get match, player names, and rankings data
atp_match_dat = read.csv('../complete_match_info_fixed_n_months.csv', header = T, 
                         colClasses = c("character", "character", "factor", "character", "integer", "character",  "Date", "double", "double", "integer", "integer", "integer", "integer", "integer", "integer", "integer", rep("integer", 3))) %>%
  mutate(surface = case_when(surface == "Hard" ~ 1,
                           surface == "Clay" ~ 2,
                           surface == "Grass" ~ 3,
                           surface == "Carpet" ~ 1)) 

# Subset 2009 - 2017 seasons
atp_match_dat = atp_match_dat %>%
  filter(tourney_date >= '2009-01-01' & tourney_date <= '2017-12-31') %>%
  mutate(week = as.numeric(tourney_date),
         month = as.Date(paste0(strftime(tourney_date,"%Y-%m"), "-01")))
#write.csv(atp_match_dat, "../appendix/data/atp_df.csv", row.names = F)

Next we load player ranking and biographical information:

# Get rankings
rankings00s = read.csv("../tennis_atp/atp_rankings_00s.csv", header = T, colClasses = c("character", "double", "character", "double")) %>%
  mutate(ranking_date = as.Date(ranking_date, format="%Y%m%d"))
rankings10s = read.csv('../tennis_atp/atp_rankings_10s.csv', header = T, colClasses = c("character", "double", "character", "double")) %>%
  mutate(ranking_date = as.Date(ranking_date, format="%Y%m%d"))
rankings20s = read.csv('../tennis_atp/atp_rankings_20s.csv', header = T, colClasses = c("character", "double", "character", "double")) %>%
  mutate(ranking_date = as.Date(ranking_date, format="%Y%m%d"))
rankings = rbind(rankings00s, rankings10s, rankings20s)

# Get player bios
names = read.csv("../tennis_atp/atp_players.csv", header = T) %>%
  mutate(full_name = paste(name_first, name_last)) %>%
  mutate(player_id = as.character(player_id))

Now let’s load the test results from the 6 Bayesian BT models.

# # Multi-T models
# multi_t_games_test_out = do.call(rbind, readRDS("./multi_t_models/bin_games/multi_t_games_test_frames.RData")) %>%
#   rename(winner_y = w_games, n = games) %>%
#   mutate(model = "Multi-T_bin_games") %>%
#   select(-best_of)
# multi_t_sets_test_out = do.call(rbind, readRDS("./multi_t_models/bin_sets/multi_t_sets_test_frames.RData")) %>%
#   rename(winner_y = sets_won_winner, n = total_sets) %>%
#   mutate(model = "Multi-T_bin_sets") %>%
#   select(-best_of)
# multi_t_negbin_sets_test_out = do.call(rbind, readRDS("./multi_t_models/negbin_sets/multi_t_negbin_sets_test_frames.RData")) %>%
#   rename(winner_y = sets_won_loser, n = best_of) %>% 
#   mutate(model = "Multi-T_negbin_sets")
# 
# # Multi-Norm models
# multi_norm_games_test_out = do.call(rbind, readRDS("./multi_normal_models/bin_games/multi_normal_games_test_frames.RData")) %>%
#   rename(winner_y = w_games, n = games) %>%
#   mutate(model = "Multi-Norm_bin_games") %>%
#   select(-best_of)
# multi_norm_sets_test_out = do.call(rbind, readRDS("./multi_normal_models/bin_sets/multi_normal_sets_test_frames.RData")) %>%
#   rename(winner_y = sets_won_winner, n = total_sets) %>%
#   mutate(model = "Multi-Norm_bin_sets") %>%
#   select(-best_of)
# multi_norm_negbin_sets_test_out = do.call(rbind, readRDS("./multi_normal_models/negbin_sets/multi_normal_negbin_sets_test_frames.RData")) %>%
#   rename(winner_y = sets_won_loser, n = best_of) %>%
#   mutate(model = "Multi-Norm_negbin_sets")

# Multi-T models
multi_t_games_test_out = rbind(do.call(rbind, readRDS("./multi_t_models_fixed_n_months/last17_multi_t_games_test_frames.RData")),
                               do.call(rbind, readRDS("./multi_t_models_fixed_n_months/multi_t_games_test_frames.RData"))) %>%
  rename(winner_y = w_games, n = games) %>%
  mutate(model = "Multi-T_bin_games") %>%
  select(-best_of)

multi_t_sets_test_out = rbind(do.call(rbind, readRDS("./multi_t_models_fixed_n_months/last17_multi_t_sets_test_frames.RData")),
                              do.call(rbind, readRDS("./multi_t_models_fixed_n_months/multi_t_sets_test_frames.RData"))) %>%
  rename(winner_y = sets_won_winner, n = total_sets) %>%
  mutate(model = "Multi-T_bin_sets") %>%
  select(-best_of)

multi_t_negbin_sets_test_out = rbind(do.call(rbind, readRDS("./multi_t_models_fixed_n_months/last17_multi_t_negbin_sets_test_frames.RData")),
                                     do.call(rbind, readRDS("./multi_t_models_fixed_n_months/multi_t_negbin_sets_test_frames.RData"))) %>%
  rename(winner_y = sets_won_loser, n = best_of) %>%
  mutate(model = "Multi-T_negbin_sets")

# Multi-Norm models
multi_norm_games_test_out = rbind(do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/last23_multi_normal_games_test_frames.RData")),
                                  do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/multi_normal_games_test_frames.RData"))) %>%
  rename(winner_y = w_games, n = games) %>%
  mutate(model = "Multi-Norm_bin_games") %>%
  select(-best_of)

multi_norm_sets_test_out = rbind(do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/last23_multi_normal_sets_test_frames.RData")),
                                 do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/multi_normal_sets_test_frames.RData"))) %>%
  rename(winner_y = sets_won_winner, n = total_sets) %>%
  mutate(model = "Multi-Norm_bin_sets") %>%
  select(-best_of)

multi_norm_negbin_sets_test_out = rbind(do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/last23_multi_normal_negbin_sets_test_frames.RData")),
                                        do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/multi_normal_negbin_sets_test_frames.RData"))) %>%
  rename(winner_y = sets_won_loser, n = best_of) %>%
  mutate(model = "Multi-Norm_negbin_sets")

And we can also see how “vanilla” (aka default) Glicko-2 does, where we first train on the whole 2009 season, and then get month-by-month predictions for years 2010-2017, updating the ratings after each month, just as we did for the Bayesian BT models.

library(PlayerRatings)

months = sort(unique(atp_match_dat$month))

# Take the first month of 2010 as the first test month
first_test_month = atp_match_dat %>%
  filter(tourney_date >= '2010-01-01') %>%
  pull(month) %>%
  min()

test_months = months[months >= first_test_month]

max_rank = 100

# Containers
glicko_accs = rep(0, length(test_months))
glicko_ratings_list = list()
glicko_test_frames = list()

for (i in 1:length(test_months)) {  
  test_month_i = test_months[i]
  
  players_to_rate = rankings %>%
    filter(ranking_date < test_month_i, rank <= max_rank) %>%
    pull(player) %>%
    unique()
  
  # Subset train/test
  glicko_train = atp_match_dat %>%
    filter(tourney_date < test_month_i, winner_id %in% players_to_rate, loser_id %in% players_to_rate) %>%
    mutate(y = 1, month = as.numeric(month))

  glicko_test = atp_match_dat %>%
    filter(month == test_month_i, winner_id %in% players_to_rate, loser_id %in% players_to_rate) %>%
    mutate(winner_y = 1, n = 1, month = as.numeric(month))
  
  # Train the model
  glicko_out = glicko2(glicko_train %>% select(month, winner_id, loser_id, y))  # defaults
  
  # Clean up and obtain Glicko-2 ratings
  glicko_ratings = glicko_out[[1]] %>%
    mutate(Player = as.character(Player)) %>%
    inner_join(names %>% select(player_id, full_name), by = c("Player" = "player_id"))
  
  # Make Glicko-2 predictions
  # If player has played less than tng matches (15 by default), set their rating to 2200, deviation of 300 (default) and predict. 
  # gamma=0 means no player 1 advantage
  glicko_predict = predict(glicko_out, glicko_test %>% select(month, winner_id, loser_id), 
                           tng=15, trat=c(2200, 300), gamma=0)
  glicko_test$p1_win_prob = glicko_predict
  glicko_test$model = "Glicko-2"
  glicko_test$pp_p1_set_win_prob = NA
  glicko_test$pp_p1_y = NA
  
  # Compute & store Glicko-2 test accuracy
  glicko_acc = mean(glicko_predict > 0.5)
  glicko_accs[i] = glicko_acc 
  
  # Store Glicko-2 ratings
  glicko_ratings_list[[i]] = glicko_ratings
  
  # Store Glicko-2 predictions
  glicko_test_frames[[i]] = glicko_test
}

glicko_test_out = do.call(rbind, glicko_test_frames)

# Join it with, say, multi_t_games_test_out so the columns match
glicko_test_out = glicko_test_out %>%
  inner_join(multi_t_sets_test_out %>% select(winner_id, loser_id, tourney_date),
             by = c("winner_id", "loser_id", "tourney_date")) %>%
  rename(pp_p1_match_win_prob = p1_win_prob) %>%
  select(ends_with("_id"), score, set_order, winner_y, n, ends_with("_age"), contains("months"), surface, tourney_date, month, ends_with("_rank"), 
         pp_p1_set_win_prob, pp_p1_match_win_prob, pp_p1_y, model) %>%
  mutate(winner_y = NA, n = NA, pp_p1_set_win_prob = NA, pp_p1_y = NA, month = as.Date(month, origin=.Date(0)))
## Warning in inner_join(., multi_t_sets_test_out %>% select(winner_id, loser_id, : Each row in `x` is expected to match at most 1 row in `y`.
## ℹ Row 4520 of `x` matches multiple rows.
## ℹ If multiple matches are expected, set `multiple = "all"` to silence this
##   warning.
# Bind them together
test_out = rbind(multi_t_games_test_out, multi_t_sets_test_out, multi_t_negbin_sets_test_out, 
                 multi_norm_games_test_out, multi_norm_sets_test_out, multi_norm_negbin_sets_test_out,
                 glicko_test_out) %>%
  distinct(., winner_id, loser_id, tourney_date, score, model, .keep_all = T) %>%  # Eliminates one duplicated Stepanek-Troicki match from 2012-05-21. Not sure how this happened
  mutate(year = substr(tourney_date, 1, 4))
table(test_out$model)
## 
##               Glicko-2   Multi-Norm_bin_games    Multi-Norm_bin_sets 
##                  17953                  17953                  17953 
## Multi-Norm_negbin_sets      Multi-T_bin_games       Multi-T_bin_sets 
##                  17953                  17953                  17953 
##    Multi-T_negbin_sets 
##                  17953

This is great–we have 17,953 test matches, and we have predictions for each of these matches for each of the 6 Bayesian BT models as well as vanilla Glicko-2.

We now need to load betting data for the test years, 2010-2017.

# Get odds data
cols = c("Tournament", "Date", "Series", "Court", "Surface", "Round", "best_of", "Winner", "Loser", "W1", "L1", "W2","L2", "W3", "L3", "W4", "L4", "W5", "L5", "Wsets", "Lsets", "Comment", "MaxW", "MaxL", "AvgW", "AvgL")
odds = rbind(read.csv("../model_evaluation/odds_data/tennis_odds_2010.csv", header = T) %>% select(all_of(cols)),
             read.csv("../model_evaluation/odds_data/tennis_odds_2011.csv", header = T) %>% select(all_of(cols)),
             read.csv("../model_evaluation/odds_data/tennis_odds_2012.csv", header = T) %>% select(all_of(cols)),
             read.csv("../model_evaluation/odds_data/tennis_odds_2013.csv", header = T) %>% select(all_of(cols)),
             read.csv("../model_evaluation/odds_data/tennis_odds_2014.csv", header = T) %>% select(all_of(cols)),
             read.csv("../model_evaluation/odds_data/tennis_odds_2015.csv", header = T) %>% select(all_of(cols)),
             read.csv("../model_evaluation/odds_data/tennis_odds_2016.csv", header = T) %>% select(all_of(cols)),
             read.csv("../model_evaluation/odds_data/tennis_odds_2017.csv", header = T) %>% select(all_of(cols))) %>%
  filter(Comment == "Completed") %>%
  mutate(Date = as.Date(Date, format = "%m/%d/%y"),
         surface = case_when(Surface == "Hard" ~ 1,
                             Surface == "Clay" ~ 2,
                             Surface == "Grass" ~ 3),
         score = case_when(best_of == 3 & (Wsets == 2 & Lsets == 0) ~ paste(paste(W1, L1, sep="-"), paste(W2, L2, sep="-")),
                           best_of == 3 & (Wsets == 2 & Lsets == 1) ~ paste(paste(paste(W1, L1, sep="-"), paste(W2, L2, sep="-")), paste(W3, L3, sep="-")),
                           best_of == 5 & (Wsets == 3 & Lsets == 0) ~ paste(paste(paste(W1, L1, sep="-"), paste(W2, L2, sep="-")), paste(W3, L3, sep="-")),
                           best_of == 5 & (Wsets == 3 & Lsets == 1) ~ paste(paste(paste(paste(W1, L1, sep="-"), paste(W2, L2, sep="-")), paste(W3, L3, sep="-")), paste(W4, L4, sep="-")),
                           best_of == 5 & (Wsets == 3 & Lsets == 2) ~ paste(paste(paste(paste(paste(W1, L1, sep="-"), paste(W2, L2, sep="-")), paste(W3, L3, sep="-")), paste(W4, L4, sep="-")), paste(W5, L5, sep="-")))) %>%
  filter(!is.na(score))

head(odds)
##               Tournament       Date Series   Court Surface     Round best_of
## 1 Brisbane International 2010-01-04 ATP250 Outdoor    Hard 1st Round       3
## 2 Brisbane International 2010-01-04 ATP250 Outdoor    Hard 1st Round       3
## 3 Brisbane International 2010-01-04 ATP250 Outdoor    Hard 1st Round       3
## 4 Brisbane International 2010-01-04 ATP250 Outdoor    Hard 1st Round       3
## 5 Brisbane International 2010-01-04 ATP250 Outdoor    Hard 1st Round       3
## 6 Brisbane International 2010-01-04 ATP250 Outdoor    Hard 1st Round       3
##        Winner         Loser W1 L1 W2 L2 W3 L3 W4 L4 W5 L5 Wsets Lsets   Comment
## 1  Gasquet R.   Nieminen J.  6  3  4  6  6  4 NA NA NA NA     2     1 Completed
## 2  Odesnik W.    Clement A.  6  4  7  6 NA NA NA NA NA NA     2     0 Completed
## 3  Gicquel M. Petzschner P.  6  3  6  1 NA NA NA NA NA NA     2     0 Completed
## 4    Falla A.     Chardy J.  6  4  6  4 NA NA NA NA NA NA     2     0 Completed
## 5     Levy H.     Llodra M.  6  2  6  0 NA NA NA NA NA NA     2     0 Completed
## 6 Bellucci T.    Chela J.I.  6  3  3  6  6  1 NA NA NA NA     2     1 Completed
##   MaxW MaxL AvgW AvgL surface       score
## 1   NA   NA   NA   NA       1 6-3 4-6 6-4
## 2   NA   NA   NA   NA       1     6-4 7-6
## 3   NA   NA   NA   NA       1     6-3 6-1
## 4   NA   NA   NA   NA       1     6-4 6-4
## 5   NA   NA   NA   NA       1     6-2 6-0
## 6   NA   NA   NA   NA       1 6-3 3-6 6-1

Great. Now we define some deterministic prediction functions and a betting function.

# Gets set win probability given game win probability
compute_set_win_prob_given_g = function(game_win_prob) {
  set_win_prob = game_win_prob^6*(1 + 
                                    6*(1-game_win_prob) + 
                                    21*(1-game_win_prob)^2 + 
                                    56*(1-game_win_prob)^3 + 
                                    126*(1-game_win_prob)^4 + 
                                    252*game_win_prob*(1-game_win_prob)^5 + 
                                    504*(1-game_win_prob)^6*game_win_prob)
  return(set_win_prob)
}

# Computes match win probability given set win probability and best of (3 or 5)
compute_match_win_prob_given_s = function(set_win_prob, best_of) {
  if (best_of == 3) {
    match_win_prob = set_win_prob^2 + 2 * set_win_prob^2 * (1-set_win_prob) 
  } else {  # best of 5
    match_win_prob = set_win_prob^3*(1 + 3*(1-set_win_prob) + 6*(1-set_win_prob)^2)
  }
  return(match_win_prob)
}

# Computes expected payouts from betting on player 1 and player 2 given respective odds and probabilities
compute_expected_payout = function(o1, o2, p1, p2) {
  # Expected payout betting one unit on p1
  E1 = (o1 - 1)*p1 - 1*p2
  # Expected payout betting one unit on p2
  E2 = (o2 - 1)*p2 - 1*p1
  return(list(E1, E2))
}

# Betting function returning profit from betting. If we don't bet, returns 0
bet_profit = function(E_payout_bet_on_winner, E_payout_bet_on_loser, threshold, odds_w, odds_l) {
  best_payout = max(E_payout_bet_on_winner, E_payout_bet_on_loser)
  if ((E_payout_bet_on_winner == best_payout) & (E_payout_bet_on_winner >= threshold)) {
    return(odds_w - 1)
  } else if ((E_payout_bet_on_loser == best_payout) & (E_payout_bet_on_loser >= threshold)) {
    return(-1)
  } else {
    return(0)
  }
}

And some string manipulation functions:

# Function takes a name and index and returns last name
get_last_name = function(name, idx) {
  return(str_split(name, " ")[[1]][idx])
}

We can make some plots of the win probability distributions:

ggplot(test_out, aes(model, pp_p1_match_win_prob)) +
  geom_boxplot() +
  ggtitle("Distribution of Winner Probs by Model") +
  scale_x_discrete(guide = guide_axis(angle = 90))

ggplot(test_out, aes(pp_p1_match_win_prob)) +
  geom_histogram() +
  facet_wrap(~model) +
  ggtitle("Distribution of Winner Probs by Model")
## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

Now we can join the bound-together test data with the odds data:

# Get player names
test_out = test_out %>%
  left_join(names %>% dplyr::select(player_id, full_name), by=c('winner_id' = 'player_id')) %>%
  left_join(names %>% dplyr::select(player_id, full_name), by=c('loser_id' = 'player_id'), suffix=c("_winner", "_loser"))
# Do some string manipulation
test_out$winner_last = sapply(test_out$full_name_winner, get_last_name, 2)
test_out$loser_last = sapply(test_out$full_name_loser, get_last_name, 2)
odds$winner_last = sapply(odds$Winner, get_last_name, 1)
odds$loser_last = sapply(odds$Loser, get_last_name, 1)
test_out$score2 = str_replace_all(test_out$score, "\\(\\d+\\)", "")

# Join test data with odds data
test_out_odds = test_out %>%
  inner_join(odds %>% select(winner_last, loser_last, surface, score, Date, MaxW, MaxL, AvgW, AvgL), 
             by = c("winner_last", "loser_last", "surface", "score2" = "score")) %>%
  filter(abs(tourney_date - Date) <= 14) %>%
  distinct(winner_id, loser_id, Date, model, .keep_all = T) %>%
  select(-c(Date, winner_last, loser_last)) %>%
  drop_na(MaxW, MaxL, AvgW, AvgL) %>%
  filter(MaxL < 1000)  # data quality issue
## Warning in inner_join(., odds %>% select(winner_last, loser_last, surface, : Each row in `x` is expected to match at most 1 row in `y`.
## ℹ Row 5 of `x` matches multiple rows.
## ℹ If multiple matches are expected, set `multiple = "all"` to silence this
##   warning.
table(test_out_odds$model)
## 
##               Glicko-2   Multi-Norm_bin_games    Multi-Norm_bin_sets 
##                  14257                  14257                  14257 
## Multi-Norm_negbin_sets      Multi-T_bin_games       Multi-T_bin_sets 
##                  14257                  14257                  14257 
##    Multi-T_negbin_sets 
##                  14257
# Check for duplicates
# 14 Matches with winner / loser:
# 104571 / 103843
# 104926 / 103163
# are okay since they played twice within 2 weeks on the same surface and had the same score!
# Otherwise a match should be duplicated no more than 7 times since we are comparing 7 models for each match.

dupes = test_out_odds %>%
  group_by(winner_id, loser_id, score, tourney_date) %>%
  summarize(num_dupe = n())
## `summarise()` has grouped output by 'winner_id', 'loser_id', 'score'. You can
## override using the `.groups` argument.
dupes %>%
  arrange(desc(num_dupe))
## # A tibble: 14,255 × 5
## # Groups:   winner_id, loser_id, score [14,163]
##    winner_id loser_id score           tourney_date num_dupe
##    <chr>     <chr>    <fct>           <date>          <int>
##  1 104571    103843   6-3 6-4         2010-05-02         14
##  2 104926    103163   6-2 6-4         2013-07-08         14
##  3 100644    103565   6-1 3-6 6-1 6-4 2016-05-23          7
##  4 100644    103582   6-7(2) 6-2 7-5  2016-02-01          7
##  5 100644    103813   6-4 6-4         2015-06-15          7
##  6 100644    103819   6-3 6-4         2017-08-07          7
##  7 100644    103819   7-6(4) 5-7 6-3  2016-06-13          7
##  8 100644    103852   6-0 6-4         2017-04-17          7
##  9 100644    103893   6-3 6-2         2017-06-19          7
## 10 100644    103898   6-0 6-4         2017-06-12          7
## # … with 14,245 more rows

So now with odds data we’re down to 14,257 test matches, so we’ve lost some matches with missing odds or questionably high payouts, but that’s okay, we still have plenty.

Let’s just run a check that the join worked correctly–we will check that the matches in test_out_odds are all in test_out–and we know this latter data frame is correct.

# Check matches in test_out_odds are in test_out
all(do.call(paste0, test_out_odds[, c("winner_id", "loser_id", "surface", "tourney_date")]) %in% do.call(paste0, test_out[, c("winner_id", "loser_id", "surface", "tourney_date")]) == T)
## [1] TRUE

Nice!

Now for the fun part– we can start collecting Brier scores:

brier_list = list("model" = rep(0, length(unique(test_out_odds$model)) + 2),
                  "brier_score" = rep(0, length(unique(test_out_odds$model)) + 2))  # Add 2 for the odds later
# Compute Brier scores for models
for (i in 1:length(unique(test_out_odds$model))) {
  model_name = unique(test_out_odds$model)[i]
  brier = mean((test_out_odds %>% filter(model == model_name) %>% pull(pp_p1_match_win_prob) - 1)^2)
  brier_list$model[i] = model_name
  brier_list$brier_score[i] = brier
}

# Compute Brier score for betting odds
one_set_test = test_out_odds %>%
  filter(model == "Multi-Norm_bin_sets") %>%
  mutate(winner_implied_prob_best_odds = (1/MaxW) / (1/MaxW + 1/MaxL),
         winner_implied_prob_avg_odds = (1/AvgW)/ (1/AvgW + 1/AvgL))
brier_best = mean((one_set_test$winner_implied_prob_best_odds - 1)^2)
brier_avg = mean((one_set_test$winner_implied_prob_avg_odds - 1)^2)
brier_list$model[length(unique(test_out_odds$model)) + 1] = "Best_odds"
brier_list$model[length(unique(test_out_odds$model)) + 2] = "Avg_odds"
brier_list$brier_score[length(unique(test_out_odds$model)) + 1] = brier_best
brier_list$brier_score[length(unique(test_out_odds$model)) + 2] = brier_avg

brier_df = as.data.frame(brier_list)
brier_df %>%
  arrange(desc(brier_score))
##                    model brier_score
## 1 Multi-Norm_negbin_sets   0.2100230
## 2    Multi-T_negbin_sets   0.2099459
## 3               Glicko-2   0.2058700
## 4    Multi-Norm_bin_sets   0.2046113
## 5       Multi-T_bin_sets   0.2045626
## 6   Multi-Norm_bin_games   0.2032697
## 7      Multi-T_bin_games   0.2032619
## 8               Avg_odds   0.1902936
## 9              Best_odds   0.1897945

The Brier scores for the games models are the best, but they don’t beat the betting lines.

Now we can find the expected payouts using our models’ probabilities.

test_out_odds$best_winner_exp_payout = 0 
test_out_odds$best_loser_exp_payout = 0
test_out_odds$avg_winner_exp_payout = 0 
test_out_odds$avg_loser_exp_payout = 0
for (i in 1:nrow(test_out_odds)) {
  best_exp_payouts_i = compute_expected_payout(test_out_odds$MaxW[i], test_out_odds$MaxL[i], test_out_odds$pp_p1_match_win_prob[i], 1-test_out_odds$pp_p1_match_win_prob[i])
  test_out_odds$best_winner_exp_payout[i] = best_exp_payouts_i[[1]]
  test_out_odds$best_loser_exp_payout[i] = best_exp_payouts_i[[2]]
  avg_exp_payouts_i = compute_expected_payout(test_out_odds$AvgW[i], test_out_odds$AvgL[i], test_out_odds$pp_p1_match_win_prob[i], 1-test_out_odds$pp_p1_match_win_prob[i])
  test_out_odds$avg_winner_exp_payout[i] = avg_exp_payouts_i[[1]]
  test_out_odds$avg_loser_exp_payout[i] = avg_exp_payouts_i[[2]]
}

head(test_out_odds %>% arrange(desc(best_winner_exp_payout)))
##   winner_id loser_id       score set_order winner_y  n winner_age loser_age
## 1    104386   105379 4-6 6-2 6-2       011        1  3   28.52567  23.45517
## 2    104386   105379 4-6 6-2 6-2       011        1  3   28.52567  23.45517
## 3    104386   105379 4-6 6-2 6-2       011        2  3   28.52567  23.45517
## 4    104386   105379 4-6 6-2 6-2       011        2  3   28.52567  23.45517
## 5    104386   105379 4-6 6-2 6-2       011       16 26   28.52567  23.45517
## 6    104386   105379 4-6 6-2 6-2       011       16 26   28.52567  23.45517
##   N_months_since_last_match_winner N_months_since_last_match_loser surface
## 1                                0                               0       1
## 2                                0                               0       1
## 3                                0                               0       1
## 4                                0                               0       1
## 5                                0                               0       1
## 6                                0                               0       1
##   tourney_date      month winner_rank loser_rank pp_p1_set_win_prob
## 1   2012-12-31 2012-12-01           9         86          0.7461498
## 2   2012-12-31 2012-12-01           9         86          0.7445691
## 3   2012-12-31 2012-12-01           9         86          0.7230098
## 4   2012-12-31 2012-12-01           9         86          0.7210667
## 5   2012-12-31 2012-12-01           9         86          0.7183128
## 6   2012-12-31 2012-12-01           9         86          0.7124635
##   pp_p1_match_win_prob pp_p1_y                  model year full_name_winner
## 1            0.8291130       1    Multi-T_negbin_sets 2012 Janko Tipsarevic
## 2            0.8266426       1 Multi-Norm_negbin_sets 2012 Janko Tipsarevic
## 3            0.8018225       2    Multi-Norm_bin_sets 2012 Janko Tipsarevic
## 4            0.8001933       2       Multi-T_bin_sets 2012 Janko Tipsarevic
## 5            0.7986466      23   Multi-Norm_bin_games 2012 Janko Tipsarevic
## 6            0.7918009      23      Multi-T_bin_games 2012 Janko Tipsarevic
##   full_name_loser      score2 MaxW MaxL AvgW AvgL best_winner_exp_payout
## 1    Aljaz Bedene 4-6 6-2 6-2  6.7 1.17 5.44 1.14               4.555057
## 2    Aljaz Bedene 4-6 6-2 6-2  6.7 1.17 5.44 1.14               4.538505
## 3    Aljaz Bedene 4-6 6-2 6-2  6.7 1.17 5.44 1.14               4.372210
## 4    Aljaz Bedene 4-6 6-2 6-2  6.7 1.17 5.44 1.14               4.361295
## 5    Aljaz Bedene 4-6 6-2 6-2  6.7 1.17 5.44 1.14               4.350932
## 6    Aljaz Bedene 4-6 6-2 6-2  6.7 1.17 5.44 1.14               4.305066
##   best_loser_exp_payout avg_winner_exp_payout avg_loser_exp_payout
## 1            -0.8000622              3.510375           -0.8051888
## 2            -0.7971718              3.496936           -0.8023725
## 3            -0.7681323              3.361914           -0.7740776
## 4            -0.7662261              3.353051           -0.7722203
## 5            -0.7644165              3.344637           -0.7704571
## 6            -0.7564071              3.307397           -0.7626531
# Get max expected payout
test_out_odds$max_exp_payout = apply(test_out_odds[, c("best_winner_exp_payout", "best_loser_exp_payout")], 1, max)
test_out_odds$avg_exp_payout = apply(test_out_odds[, c("avg_winner_exp_payout", "avg_loser_exp_payout")], 1, max)

We have the maximum expected payouts given by the best odds and average odds for each model. Now we can try betting on matches when the expected payout given by the model is larger than some threshold. The thresholds I will try are {0, 0.01, 0.02, …, 2.54, 2.55, …, 5.98, 5.99, 6}.

# Try a bunch of other thresholds
t = seq(0, 6, by = 0.01)
best_odds_profits = list()
avg_odds_profits = list()
best_odds_bets_placed = list()
avg_odds_bets_placed = list()
years = list()
for (i in 1:length(t)) {
  test_out_odds$best_odds_profit = mapply(bet_profit, test_out_odds$best_winner_exp_payout, test_out_odds$best_loser_exp_payout, t[i], test_out_odds$MaxW, test_out_odds$MaxL)
  test_out_odds$avg_odds_profit = mapply(bet_profit, test_out_odds$avg_winner_exp_payout, test_out_odds$avg_loser_exp_payout, t[i], test_out_odds$AvgW, test_out_odds$AvgL)
  grp = test_out_odds %>%
    group_by(model, year) %>%
    summarize(best_odds_net_profit = sum(best_odds_profit), best_odds_n_bets = sum(best_odds_profit != 0), best_odds_return = best_odds_net_profit / best_odds_n_bets,
            avg_odds_net_profit = sum(avg_odds_profit), avg_odds_n_bets = sum(avg_odds_profit != 0), avg_odds_return = avg_odds_net_profit / avg_odds_n_bets)
  best_odds_profits[[i]] = grp$best_odds_net_profit
  names(best_odds_profits[[i]]) = grp$model
  avg_odds_profits[[i]] = grp$avg_odds_net_profit
  names(avg_odds_profits[[i]]) = grp$model
  best_odds_bets_placed[[i]] = grp$best_odds_n_bets
  names(best_odds_bets_placed[[i]]) = grp$model
  avg_odds_bets_placed[[i]] = grp$avg_odds_n_bets
  names(avg_odds_bets_placed[[i]]) = grp$model
  years[[i]] = grp$year
  names(years[[i]]) = grp$model
}
# Clean up results and put them into a "profit" data frame
n_models = length(unique(test_out_odds$model))
n_test_years = length(unique(test_out_odds$year))
profit_df = data.frame(best_odds_profit = unlist(best_odds_profits), best_odds_bets_placed = unlist(best_odds_bets_placed), 
                       avg_odds_profit = unlist(avg_odds_profits), avg_odds_bets_placed = unlist(avg_odds_bets_placed),
                       model = names(unlist(best_odds_profits)), thresh = rep(t, each=n_models*n_test_years), year=unlist(years))
profit_df %>%
  slice(20:30)
##    best_odds_profit best_odds_bets_placed avg_odds_profit avg_odds_bets_placed
## 1             84.48                  1849         -127.87                 1403
## 2             12.40                  1751          -76.48                 1391
## 3            -58.22                  1800         -152.76                 1446
## 4            -29.81                  1794         -165.62                 1501
## 5             -2.55                  1827         -106.81                 1532
## 6            -13.14                  1226          -70.08                 1046
## 7            -58.29                  1849         -126.92                 1561
## 8             48.07                  1879          -21.97                 1492
## 9             -6.50                  1851          -88.83                 1526
## 10             7.19                  1765          -73.84                 1523
## 11           -67.24                  1832         -107.71                 1546
##                     model thresh year
## 1     Multi-Norm_bin_sets      0 2013
## 2     Multi-Norm_bin_sets      0 2014
## 3     Multi-Norm_bin_sets      0 2015
## 4     Multi-Norm_bin_sets      0 2016
## 5     Multi-Norm_bin_sets      0 2017
## 6  Multi-Norm_negbin_sets      0 2010
## 7  Multi-Norm_negbin_sets      0 2011
## 8  Multi-Norm_negbin_sets      0 2012
## 9  Multi-Norm_negbin_sets      0 2013
## 10 Multi-Norm_negbin_sets      0 2014
## 11 Multi-Norm_negbin_sets      0 2015

We can also compute a “null” model to use as a benchmark. Let’s let the null model be the model that always bets on the higher-ranked player to win.

# Just take one set of test matches (don't want to overcount)
# Replace NA ranks with Inf
one_set_test_matches = test_out_odds %>%
  filter(model == "Multi-Norm_bin_sets") %>%
  mutate(winner_rank = ifelse(is.na(winner_rank), Inf, winner_rank),
         loser_rank = ifelse(is.na(loser_rank), Inf, loser_rank))

null_model_results = one_set_test_matches %>%
  mutate(best_odds_profit = case_when(winner_rank < loser_rank ~ MaxW - 1,
                                 loser_rank < winner_rank ~ -1,
                                 TRUE ~ 0),
         avg_odds_profit = case_when(winner_rank < loser_rank ~ AvgW - 1,
                                 loser_rank < winner_rank ~ -1,
                                 TRUE ~ 0),
         model = 'null')

null_model_results_by_year = null_model_results %>%
  group_by(year) %>%
  summarize(best_odds_bets_placed = sum(best_odds_profit != 0),
            avg_odds_bets_placed = sum(avg_odds_profit != 0),
            best_odds_profit = sum(best_odds_profit),
            avg_odds_profit = sum(avg_odds_profit),
            model = 'null')
null_model_results_by_year$thresh = seq(0, 6, length=n_test_years)

sum(null_model_results$best_odds_profit)
## [1] 47.59
sum(null_model_results$avg_odds_profit)
## [1] -659.59

We can also plot the profit of each model by year.

model.labs = c("1.(a)", "1.(b)", "2.(a)", "2.(b)", "3.(a)", "3.(b)", "Glicko-2", "null")
names(model.labs) = c("Multi-Norm_bin_games", "Multi-T_bin_games", "Multi-Norm_bin_sets", "Multi-T_bin_sets", "Multi-Norm_negbin_sets", "Multi-T_negbin_sets", "Glicko-2", "null")
# PLOT year over year profits
ggplot(profit_df %>% filter(model %in% c("Glicko-2", "Multi-Norm_bin_games", "Multi-T_bin_games")), aes(thresh, best_odds_profit, color=year)) + 
  geom_line() +
  labs(x="Betting threshold (E)", y="Profit (units)", title="Betting with best odds available") +
  geom_hline(data=null_model_results_by_year, aes(yintercept=best_odds_profit, color=year)) +
  facet_wrap(~model, nrow=2, labeller = labeller(model = model.labs)) +
  ylim(-150, 150)
## Warning: Removed 5 rows containing missing values (`geom_line()`).

ggsave("../manuscript/first_draft/images/year_over_year_profits_best_odds.png")
## Saving 10 x 5 in image
## Warning: Removed 5 rows containing missing values (`geom_line()`).
ggplot(profit_df %>% filter(model %in% c("Glicko-2", "Multi-Norm_bin_games", "Multi-T_bin_games")), aes(thresh, avg_odds_profit, color=year)) + 
  geom_line() +
  labs(x="Betting threshold (E)", y="Profit (units)", title="Betting with average odds available") + 
  geom_hline(data=null_model_results_by_year, aes(yintercept=avg_odds_profit, color=year)) +
  facet_wrap(~model, nrow=2, labeller = labeller(model = model.labs)) +
  ylim(-150, 25)
## Warning: Removed 34 rows containing missing values (`geom_line()`).

ggsave("../manuscript/first_draft/images/year_over_year_profits_average_odds.png")
## Saving 10 x 5 in image
## Warning: Removed 34 rows containing missing values (`geom_line()`).
# Compute AUCs
library(DescTools)

auc_mat = matrix(nrow = length(unique(profit_df$model)), ncol = length(unique(profit_df$year)))
models = unique(profit_df$model)
years = unique(profit_df$year)


for (i in 1:length(models)) {
  for (j in 1:length(years)) {
    filtered_profit_df = profit_df %>% filter(model == models[i], year == years[j])
    auc_mat[i, j] = AUC(filtered_profit_df$thresh, filtered_profit_df$best_odds_profit)
  }
}

auc_df = as.data.frame(t(auc_mat))
auc_df$year = years
colnames(auc_df) = c(models, "year")
auc_df
##     Glicko-2 Multi-Norm_bin_games Multi-Norm_bin_sets Multi-Norm_negbin_sets
## 1  -78.53715             -3.86770           -55.93015              -60.35340
## 2 -194.68995           -130.64220           -98.90420              -64.71215
## 3  -26.00890            156.81205            -8.00340               32.71205
## 4   41.71595            256.22880            90.50700               -1.19230
## 5  -60.79195            -49.04570           -26.72420              -17.05815
## 6  -74.04365           -100.99215           -62.73490              -29.96160
## 7  -98.13105             33.56080            29.90155               -0.77220
## 8  -50.42030              6.12715            18.47745               22.34105
##   Multi-T_bin_games Multi-T_bin_sets Multi-T_negbin_sets year
## 1          -6.40460        -66.33595           -64.98315 2010
## 2        -125.41945        -94.74150           -64.41610 2011
## 3         125.38110        -17.24140            31.52040 2012
## 4         243.86910         84.63975            -0.93835 2013
## 5         -48.94905        -28.76840           -16.04880 2014
## 6        -104.41130        -67.10950           -31.05420 2015
## 7          37.75345         30.45020            -0.11505 2016
## 8           5.36635         19.38520            22.99750 2017
# Summary statistics
summary(auc_df %>% select(-year)) 
##     Glicko-2       Multi-Norm_bin_games Multi-Norm_bin_sets
##  Min.   :-194.69   Min.   :-130.64      Min.   :-98.90     
##  1st Qu.: -83.44   1st Qu.: -62.03      1st Qu.:-57.63     
##  Median : -67.42   Median :   1.13      Median :-17.36     
##  Mean   : -67.61   Mean   :  21.02      Mean   :-14.18     
##  3rd Qu.: -44.32   3rd Qu.:  64.37      3rd Qu.: 21.33     
##  Max.   :  41.72   Max.   : 256.23      Max.   : 90.51     
##  Multi-Norm_negbin_sets Multi-T_bin_games   Multi-T_bin_sets
##  Min.   :-64.712        Min.   :-125.4194   Min.   :-94.74  
##  1st Qu.:-37.560        1st Qu.: -62.8146   1st Qu.:-66.53  
##  Median : -9.125        Median :  -0.5191   Median :-23.00  
##  Mean   :-14.875        Mean   :  15.8982   Mean   :-17.47  
##  3rd Qu.:  5.006        3rd Qu.:  59.6604   3rd Qu.: 22.15  
##  Max.   : 32.712        Max.   : 243.8691   Max.   : 84.64  
##  Multi-T_negbin_sets
##  Min.   :-64.983    
##  1st Qu.:-39.395    
##  Median : -8.494    
##  Mean   :-15.380    
##  3rd Qu.:  5.663    
##  Max.   : 31.520
# Get null model areas
null_model_results_by_year$AUC = 6*null_model_results_by_year$best_odds_profit
summary(null_model_results_by_year$AUC)
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
## -191.22 -182.18   46.62   35.69  163.57  385.08

And get cumulative profits by summing over the years.

# Now get cumulative profit by summing over the years

# For the models
cum_profit_df = profit_df %>% 
  group_by(model, thresh) %>% 
  summarize(best_odds_profit = sum(best_odds_profit),
            avg_odds_profit = sum(avg_odds_profit),
            best_odds_bets_placed = sum(best_odds_bets_placed),
            avg_odds_bets_placed = sum(avg_odds_bets_placed))
## `summarise()` has grouped output by 'model'. You can override using the
## `.groups` argument.
# For the null model
cum_null_model_results = null_model_results_by_year %>%
  group_by(model) %>%
  summarize(best_odds_profit = sum(best_odds_profit),
            avg_odds_profit = sum(avg_odds_profit),
            best_odds_bets_placed = sum(best_odds_bets_placed),
            avg_odds_bets_placed = sum(avg_odds_bets_placed))

cum_profit_df %>%
  arrange(desc(best_odds_profit))
## # A tibble: 4,207 × 6
## # Groups:   model [7]
##    model                thresh best_odds_profit avg_odds_profit best_o…¹ avg_o…²
##    <chr>                 <dbl>            <dbl>           <dbl>    <int>   <int>
##  1 Multi-Norm_bin_games   1.91             180.          -11.9       169      38
##  2 Multi-Norm_bin_games   1.93             180.           -7.94      165      34
##  3 Multi-Norm_bin_games   1.92             179.           -9.94      166      36
##  4 Multi-Norm_bin_games   2.23             178.            5.09      103      17
##  5 Multi-Norm_bin_games   1.89             178.          -11.9       172      38
##  6 Multi-Norm_bin_games   1.9              178.          -11.9       172      38
##  7 Multi-Norm_bin_games   1.95             177.           -5.94      159      32
##  8 Multi-Norm_bin_games   2.22             177.            5.09      104      17
##  9 Multi-T_bin_games      1.86             176.          -12.9       177      39
## 10 Multi-T_bin_games      1.9              176.           -9.94      168      36
## # … with 4,197 more rows, and abbreviated variable names
## #   ¹​best_odds_bets_placed, ²​avg_odds_bets_placed

We plot the cumulative profits now.

library(scales)
## 
## Attaching package: 'scales'
## The following object is masked from 'package:purrr':
## 
##     discard
## The following object is masked from 'package:readr':
## 
##     col_factor
colors = hue_pal()(8)
# PLOT cumulative profits
ggplot(cum_profit_df, aes(thresh, best_odds_profit, color=model)) + 
  geom_line() +
  labs(x="Betting threshold (E)", y="Profit (units)", title="Betting with best odds available") +
  geom_hline(data=cum_null_model_results, aes(yintercept=best_odds_profit, color=model)) +
  scale_color_manual(labels = model.labs, values = colors)

ggsave("../manuscript/first_draft/images/cumulative_profits_best_odds.png")
## Saving 5 x 3 in image
ggplot(cum_profit_df, aes(thresh, avg_odds_profit, color=model)) + 
  geom_line() +
  labs(x="Betting threshold (E)", y="Profit (units)", title="Betting with average odds available") +
  geom_hline(data=cum_null_model_results, aes(yintercept=avg_odds_profit, color=model)) +
  scale_color_manual(labels = model.labs, values = colors)

ggsave("../manuscript/first_draft/images/cumulative_profits_average_odds.png")
## Saving 5 x 3 in image

Note, however, in a true betting model we must pick the threshold in advance. So, in the style of McHale & Morton (2010), we can pick the threshold for the betting strategy iteratively. Since we have forecasts for 2010-2012, first we can find the best threshold for these months, use this threshold to make bets on 2013, then use 2011-2013’s best threshold to make bets on 2014, etc, until 2017.

Let’s implement this:

# Find best threshold in given year vector for each model
find_best_thresh_by_year_for_each_model = function(given_years) {
  best_thresh_by_model = profit_df %>%
    filter(year %in% as.character(given_years)) %>%
    group_by(model, thresh) %>%
    summarize(best_odds_profit = sum(best_odds_profit)) %>% # Do sum(avg_odds_profit) for average odds available
    arrange(desc(best_odds_profit)) %>%
    summarize(thresh = first(thresh)) %>%
    arrange(model)
  return(best_thresh_by_model)
  # COULD DO A (WEIGHTED) AVERAGE OF PRIOR YEARS PROFITS, E.G.
  # best_thresh_by_year_by_model = profit_df %>%
  #   #filter(year %in% c(as.character(as.numeric(given_year)),  as.character(as.numeric(given_year) - 1))) %>%
  #   filter(year <= given_year) %>%
  #   group_by(model, year) %>%
  #   arrange(desc(best_odds_profit)) %>%
  #   summarize(thresh = first(thresh), profit = first(best_odds_profit)) %>%
  #   ungroup(year) %>%
  #   mutate(avg_thresh = mean(thresh)) %>%
  #   group_by(model) %>%
  #   summarize(thresh = round(first(avg_thresh), 2))
  #return(best_thresh_by_year_by_model)
}

find_best_thresh_by_year_for_each_model(2010:2012)
## # A tibble: 7 × 2
##   model                  thresh
##   <chr>                   <dbl>
## 1 Glicko-2                 5.85
## 2 Multi-Norm_bin_games     1.39
## 3 Multi-Norm_bin_sets      0   
## 4 Multi-Norm_negbin_sets   0.25
## 5 Multi-T_bin_games        1.86
## 6 Multi-T_bin_sets         4.35
## 7 Multi-T_negbin_sets      0.19

First let’s add the month to the posterior mean data frames. We will add these values to the test data frames for inspection.

# LOAD POSTERIOR MEAN DFs
# Multi-T
multi_t_games_post_mean_dfs = c(readRDS("./multi_t_models_fixed_n_months/multi_t_games_post_mean_dfs.RData"),
                                   readRDS("./multi_t_models_fixed_n_months/last17_multi_t_games_post_mean_dfs.RData"))
multi_t_sets_post_mean_dfs = c(readRDS("./multi_t_models_fixed_n_months/multi_t_sets_post_mean_dfs.RData"),
                               readRDS("./multi_t_models_fixed_n_months/last17_multi_t_sets_post_mean_dfs.RData"))
multi_t_negbin_sets_post_mean_dfs = c(readRDS("./multi_t_models_fixed_n_months/multi_t_negbin_sets_post_mean_dfs.RData"),
                                      readRDS("./multi_t_models_fixed_n_months/last17_multi_t_negbin_sets_post_mean_dfs.RData"))
# Multi-Norm
multi_norm_games_post_mean_dfs = c(readRDS("./multi_normal_models_fixed_n_months/last23_multi_normal_games_post_mean_dfs.RData"),
                                   readRDS("./multi_normal_models_fixed_n_months/multi_normal_games_post_mean_dfs.RData"))
multi_norm_sets_post_mean_dfs = c(readRDS("./multi_normal_models_fixed_n_months/last23_multi_normal_sets_post_mean_dfs.RData"),
                                  readRDS("./multi_normal_models_fixed_n_months/multi_normal_sets_post_mean_dfs.RData"))
multi_norm_negbin_sets_post_mean_dfs = c(readRDS("./multi_normal_models_fixed_n_months/last23_multi_normal_negbin_sets_post_mean_dfs.RData"),
                                         readRDS("./multi_normal_models_fixed_n_months/multi_normal_negbin_sets_post_mean_dfs.RData"))

# First let's add the month to the posterior mean dfs
for (i in 1:length(test_months)) {
  multi_norm_games_post_mean_dfs[[i]]$month = test_months[i]
  multi_norm_games_post_mean_dfs[[i]]$model = "Multi-Norm_bin_games"
  multi_norm_sets_post_mean_dfs[[i]]$month = test_months[i]
  multi_norm_sets_post_mean_dfs[[i]]$model = "Multi-Norm_bin_sets"
  multi_norm_negbin_sets_post_mean_dfs[[i]]$month = test_months[i]
  multi_norm_negbin_sets_post_mean_dfs[[i]]$model = "Multi-Norm_negbin_sets"
  multi_t_games_post_mean_dfs[[i]]$month = test_months[i]
  multi_t_games_post_mean_dfs[[i]]$model = "Multi-T_bin_games"
  multi_t_sets_post_mean_dfs[[i]]$month = test_months[i]
  multi_t_sets_post_mean_dfs[[i]]$model = "Multi-T_bin_sets"
  multi_t_negbin_sets_post_mean_dfs[[i]]$month = test_months[i]
  multi_t_negbin_sets_post_mean_dfs[[i]]$model = "Multi-T_negbin_sets"
}


multi_t_games_post_mean_dfs = do.call(rbind, multi_t_games_post_mean_dfs)
multi_t_sets_post_mean_dfs = do.call(rbind, multi_t_sets_post_mean_dfs)
multi_t_negbin_sets_post_mean_dfs = do.call(rbind, multi_t_negbin_sets_post_mean_dfs)
multi_norm_games_post_mean_dfs = do.call(rbind, multi_norm_games_post_mean_dfs)
multi_norm_sets_post_mean_dfs = do.call(rbind, multi_norm_sets_post_mean_dfs)
multi_norm_negbin_sets_post_mean_dfs = do.call(rbind, multi_norm_negbin_sets_post_mean_dfs)

# Now we bind them together so we can join them with the test matches
posterior_mean_frames = rbind(multi_t_games_post_mean_dfs, multi_t_sets_post_mean_dfs, multi_norm_games_post_mean_dfs, multi_norm_sets_post_mean_dfs,
                                         multi_norm_negbin_sets_post_mean_dfs, multi_t_negbin_sets_post_mean_dfs)
wide_posterior_mean_frames = pivot_wider(posterior_mean_frames,
            id_cols = c(player_id, full_name, month, model),
            names_from = skill_type,
            values_from = c(starts_with("posterior"), ends_with("_q")))
head(wide_posterior_mean_frames)
## # A tibble: 6 × 19
## # Groups:   player_id, full_name [6]
##   player_id full_n…¹ month      model poster…² poster…³ poster…⁴ poste…⁵ poste…⁶
##   <chr>     <chr>    <date>     <chr>    <dbl>    <dbl>    <dbl>   <dbl>   <dbl>
## 1 101868    Dick No… 2010-01-01 Mult… -0.0153  -0.0184  -0.0203    0.188  0.173 
## 2 101962    Younes … 2010-01-01 Mult…  0.00595  0.00832  0.00923   0.229  0.220 
## 3 102148    Fabrice… 2010-01-01 Mult… -0.0657   0.0292   0.0104    0.114  0.0775
## 4 102318    Andrei … 2010-01-01 Mult… -0.215   -0.213   -0.230     0.167  0.148 
## 5 102434    Vincent… 2010-01-01 Mult… -0.318   -0.309   -0.352     0.179  0.131 
## 6 102563    Thomas … 2010-01-01 Mult… -0.0189  -0.0164  -0.0201    0.167  0.145 
## # … with 10 more variables: posterior_sd_hard_skill <dbl>,
## #   posterior_median_clay_skill <dbl>, posterior_median_grass_skill <dbl>,
## #   posterior_median_hard_skill <dbl>, lower.025_q_clay_skill <dbl>,
## #   lower.025_q_grass_skill <dbl>, lower.025_q_hard_skill <dbl>,
## #   upper.975_q_clay_skill <dbl>, upper.975_q_grass_skill <dbl>,
## #   upper.975_q_hard_skill <dbl>, and abbreviated variable names ¹​full_name,
## #   ²​posterior_mean_clay_skill, ³​posterior_mean_grass_skill, …
# Now run the betting experiment
test_years = seq(2013, 2017, by = 1)

res_profit = list()
res_matches_we_bet_on = list()

best_thresh_df = find_best_thresh_by_year_for_each_model(2010:2012)
best_threshes = best_thresh_df %>% pull(thresh)
model_names = best_thresh_df %>% pull(model)

for (i in 1:length(test_years)) {
  # Get the profit for each model in year test_year using the best thresh from previous year
  lst_profit = list()
  lst_matches_we_bet_on = list()
  for (j in 1:length(best_threshes)) {
    # Record profits from matches we bet on
    lst_profit[[j]] = profit_df %>% filter(model == model_names[j], 
                                    year == as.character(test_years[i]),
                                    thresh > best_threshes[j] - .005,
                                    thresh < best_threshes[j] + .005)
    # Record matches with our bets
    matches_we_bet_on = test_out_odds %>% 
      filter(model == model_names[j],
             year == as.character(test_years[i]),
             max_exp_payout >= (best_threshes[j])) %>%
             mutate(best_odds_profit = ifelse(max_exp_payout == best_winner_exp_payout, MaxW-1, -1)) %>%#,
                    #avg_odds_profit = ifelse(max_exp_payout == avg_winner_exp_payout, AvgW-1, -1)) %>%
      select(-avg_odds_profit) %>%
      inner_join(wide_posterior_mean_frames, by = c("winner_id" = "player_id", "month", "model")) %>%
      inner_join(wide_posterior_mean_frames, by = c("loser_id" = "player_id", "month", "model"), suffix = c("_winner", "_loser"))
                  
    lst_matches_we_bet_on[[j]] = matches_we_bet_on
  }
  res_profit[[i]] = do.call(rbind, lst_profit)
  res_matches_we_bet_on[[i]] = do.call(rbind, lst_matches_we_bet_on)
  
  # Update threshes, use as big a rolling window as possible
  best_threshes = find_best_thresh_by_year_for_each_model((2010):(test_years[i])) %>% pull(thresh)
}

profit_res = do.call(rbind, res_profit)
profit_res %>%
  arrange(model)
##    best_odds_profit best_odds_bets_placed avg_odds_profit avg_odds_bets_placed
## 1             -2.00                     2            0.00                    0
## 2            -17.64                    47           -4.92                   17
## 3            -32.10                    60           -2.35                   21
## 4             -9.55                    48           -2.50                   22
## 5            -17.32                    39          -23.00                   23
## 6             79.12                    50          -10.00                   10
## 7            -10.73                  1376         -111.33                  984
## 8           -104.14                  1406         -169.15                 1032
## 9             29.61                    24           -2.03                    6
## 10            -2.12                    16            4.57                    7
## 11            84.48                  1849         -127.87                 1403
## 12            12.40                  1751          -76.48                 1391
## 13           -58.22                  1800         -152.76                 1446
## 14           -29.81                  1794         -165.62                 1501
## 15            -2.55                  1827         -106.81                 1532
## 16            19.20                   709          -11.53                  462
## 17           -37.09                   516          -66.98                  330
## 18           -15.08                   869          -66.61                  626
## 19           -36.93                  1249          -67.97                  961
## 20            55.23                   545           -8.52                  403
## 21            85.00                    22           -2.00                    2
## 22            -7.00                     7           -1.00                    1
## 23           -13.25                    19           -2.92                    8
## 24            27.61                    26           -3.03                    7
## 25             1.81                    28           -0.43                   12
## 26            -1.00                     1            0.00                    0
## 27           -62.15                   737          -84.20                  482
## 28           -41.21                  1655         -150.13                 1286
## 29           -30.70                  1671         -154.82                 1334
## 30             0.96                    45           -4.58                   23
## 31            16.24                   901          -12.85                  601
## 32           -39.20                   527          -74.98                  345
## 33            -5.30                  1259          -71.15                  966
## 34           -44.08                  1304          -67.95                  998
## 35            52.53                   630          -11.02                  466
##                     model thresh year
## 1                Glicko-2   5.85 2013
## 2                Glicko-2   1.43 2014
## 3                Glicko-2   1.38 2015
## 4                Glicko-2   1.43 2016
## 5                Glicko-2   1.44 2017
## 6    Multi-Norm_bin_games   1.39 2013
## 7    Multi-Norm_bin_games   0.06 2014
## 8    Multi-Norm_bin_games   0.07 2015
## 9    Multi-Norm_bin_games   1.93 2016
## 10   Multi-Norm_bin_games   2.23 2017
## 11    Multi-Norm_bin_sets   0.00 2013
## 12    Multi-Norm_bin_sets   0.00 2014
## 13    Multi-Norm_bin_sets   0.00 2015
## 14    Multi-Norm_bin_sets   0.00 2016
## 15    Multi-Norm_bin_sets   0.00 2017
## 16 Multi-Norm_negbin_sets   0.25 2013
## 17 Multi-Norm_negbin_sets   0.30 2014
## 18 Multi-Norm_negbin_sets   0.18 2015
## 19 Multi-Norm_negbin_sets   0.10 2016
## 20 Multi-Norm_negbin_sets   0.33 2017
## 21      Multi-T_bin_games   1.86 2013
## 22      Multi-T_bin_games   1.86 2014
## 23      Multi-T_bin_games   1.86 2015
## 24      Multi-T_bin_games   1.86 2016
## 25      Multi-T_bin_games   1.86 2017
## 26       Multi-T_bin_sets   4.35 2013
## 27       Multi-T_bin_sets   0.21 2014
## 28       Multi-T_bin_sets   0.02 2015
## 29       Multi-T_bin_sets   0.02 2016
## 30       Multi-T_bin_sets   1.37 2017
## 31    Multi-T_negbin_sets   0.19 2013
## 32    Multi-T_negbin_sets   0.29 2014
## 33    Multi-T_negbin_sets   0.09 2015
## 34    Multi-T_negbin_sets   0.09 2016
## 35    Multi-T_negbin_sets   0.29 2017
# Sum over the years to get cumulative profit, bets placed, avg thresh, etc
profit_res %>%
  group_by(model) %>%
  summarize(total_profit = sum(best_odds_profit),
            total_bets_placed = sum(best_odds_bets_placed),
            average_thresh_used = mean(thresh),
            n_test_years = n(),
            avg_total_profit = sum(avg_odds_profit),
            avg_total_bets_placed = sum(avg_odds_bets_placed),
            avg_average_thresh_used = mean(thresh),
            avg_n_test_years = n()) %>%
  arrange(desc(total_profit))
## # A tibble: 7 × 9
##   model          total…¹ total…² avera…³ n_tes…⁴ avg_t…⁵ avg_t…⁶ avg_a…⁷ avg_n…⁸
##   <chr>            <dbl>   <int>   <dbl>   <int>   <dbl>   <int>   <dbl>   <int>
## 1 Multi-T_bin_g…   94.2      102   1.86        5   -9.38      30   1.86        5
## 2 Multi-Norm_bi…    6.3     9021   0           5 -630.      7273   0           5
## 3 Multi-Norm_bi…   -8.26    2872   1.14        5 -288.      2039   1.14        5
## 4 Multi-Norm_ne…  -14.7     3888   0.232       5 -222.      2782   0.232       5
## 5 Multi-T_negbi…  -19.8     4621   0.19        5 -238.      3376   0.19        5
## 6 Glicko-2        -78.6      196   2.31        5  -32.8       83   2.31        5
## 7 Multi-T_bin_s… -134.      4109   1.19        5 -394.      3125   1.19        5
## # … with abbreviated variable names ¹​total_profit, ²​total_bets_placed,
## #   ³​average_thresh_used, ⁴​n_test_years, ⁵​avg_total_profit,
## #   ⁶​avg_total_bets_placed, ⁷​avg_average_thresh_used, ⁸​avg_n_test_years

The games models are clearly best.

# See matches we bet on for the Multi-T games model
matches_res = do.call(rbind, res_matches_we_bet_on)
multi_norm_games_model_bets = matches_res %>% 
  filter(model == "Multi-Norm_bin_games") %>%
  arrange(desc(best_odds_profit))

multi_t_games_model_bets = matches_res %>% 
  filter(model == "Multi-T_bin_games") %>%
  arrange(desc(best_odds_profit))

head(multi_t_games_model_bets)
##   winner_id loser_id                    score set_order winner_y  n winner_age
## 1    104660   103819 6-7(5) 7-6(5) 7-5 7-6(5)      0111       27 51   27.46338
## 2    104327   104745        7-6(4) 7-6(8) 6-4       111       20 36   29.28131
## 3    105023   104925    7-6(6) 6-1 3-6 7-6(5)      1101       23 42   28.72279
## 4    103163   103819           2-6 7-6(8) 6-4       011       15 31   39.19233
## 5    103781   106233                  6-3 7-5        11       13 21   35.15674
## 6    103970   104755          6-3 6-4 5-7 6-2      1101       23 39   35.25257
##   loser_age N_months_since_last_match_winner N_months_since_last_match_loser
## 1  31.87680                                0                               0
## 2  27.05818                                0                               0
## 3  29.10062                                0                               0
## 4  35.84394                                0                               2
## 5  22.87201                                0                               0
## 6  31.04175                                0                               0
##   surface tourney_date      month winner_rank loser_rank pp_p1_set_win_prob
## 1       3   2013-06-24 2013-06-01         116          3          0.1963428
## 2       3   2013-06-24 2013-06-01         135          5          0.2316756
## 3       3   2016-06-27 2016-06-01          41          1          0.2376445
## 4       3   2017-06-12 2017-06-01         302          5          0.3289500
## 5       2   2016-07-18 2016-07-01         421          9          0.3836712
## 6       3   2017-07-03 2017-07-01          39         27          0.5006097
##   pp_p1_match_win_prob pp_p1_y             model year  full_name_winner
## 1           0.05876177      25 Multi-T_bin_games 2013 Sergiy Stakhovsky
## 2           0.09124023      26 Multi-T_bin_games 2013      Steve Darcis
## 3           0.09349758      26 Multi-T_bin_games 2016       Sam Querrey
## 4           0.25493412      17 Multi-T_bin_games 2017        Tommy Haas
## 5           0.32962258      18 Multi-T_bin_games 2016     Jurgen Melzer
## 6           0.50116288      32 Multi-T_bin_games 2017      David Ferrer
##   full_name_loser          score2  MaxW MaxL  AvgW AvgL best_winner_exp_payout
## 1   Roger Federer 6-7 7-6 7-5 7-6 61.00 1.01 22.96 1.01               2.584468
## 2    Rafael Nadal     7-6 7-6 6-4 46.00 1.02 20.68 1.01               3.197051
## 3  Novak Djokovic 7-6 6-1 3-6 7-6 39.75 1.02 20.78 1.01               2.716529
## 4   Roger Federer     2-6 7-6 6-4 11.88 1.08  8.92 1.06               2.028617
## 5   Dominic Thiem         6-3 7-5  9.50 1.11  7.98 1.07               2.131415
## 6 Richard Gasquet 6-3 6-4 5-7 6-2  8.50 1.15  6.65 1.11               3.259884
##   best_loser_exp_payout avg_winner_exp_payout avg_loser_exp_payout
## 1           -0.04934938             0.3491702          -0.04934938
## 2           -0.07306503             0.8868480          -0.08215263
## 3           -0.07536753             0.9428797          -0.08443256
## 4           -0.19532885             1.2740124          -0.21023017
## 5           -0.25588107             1.6303882          -0.28269616
## 6           -0.42633731             2.3327332          -0.44629080
##   max_exp_payout avg_exp_payout best_odds_profit full_name_winner_winner
## 1       2.584468      0.3491702            60.00       Sergiy Stakhovsky
## 2       3.197051      0.8868480            45.00            Steve Darcis
## 3       2.716529      0.9428797            38.75             Sam Querrey
## 4       2.028617      1.2740124            10.88              Tommy Haas
## 5       2.131415      1.6303882             8.50           Jurgen Melzer
## 6       3.259884      2.3327332             7.50            David Ferrer
##   posterior_mean_clay_skill_winner posterior_mean_grass_skill_winner
## 1                      -0.09224965                        0.07527216
## 2                      -0.05020994                        0.04085384
## 3                       0.11470588                        0.20641211
## 4                       0.29183059                        0.24895066
## 5                       0.10877617                        0.12945522
## 6                       0.53687299                        0.31236917
##   posterior_mean_hard_skill_winner posterior_sd_clay_skill_winner
## 1                       0.04494766                     0.05576709
## 2                       0.01891567                     0.06540644
## 3                       0.19285869                     0.04420291
## 4                       0.23741133                     0.04742965
## 5                       0.13044653                     0.03853420
## 6                       0.39032879                     0.02935726
##   posterior_sd_grass_skill_winner posterior_sd_hard_skill_winner
## 1                      0.05876358                     0.03687901
## 2                      0.06224883                     0.04964769
## 3                      0.03776888                     0.02607126
## 4                      0.04892136                     0.03140865
## 5                      0.04348034                     0.02933573
## 6                      0.04547992                     0.02323211
##   posterior_median_clay_skill_winner posterior_median_grass_skill_winner
## 1                        -0.09163850                          0.07459905
## 2                        -0.05003597                          0.03974190
## 3                         0.11454225                          0.20546075
## 4                         0.29097355                          0.24723133
## 5                         0.10842349                          0.12839951
## 6                         0.53658100                          0.31218640
##   posterior_median_hard_skill_winner lower.025_q_clay_skill_winner
## 1                         0.04441410                   -0.20316267
## 2                         0.01840215                   -0.17366034
## 3                         0.19248900                    0.02892250
## 4                         0.23731050                    0.19952352
## 5                         0.12904100                    0.03601524
## 6                         0.39027850                    0.48157390
##   lower.025_q_grass_skill_winner lower.025_q_hard_skill_winner
## 1                    -0.04020534                   -0.02808499
## 2                    -0.07823072                   -0.07765175
## 3                     0.13745054                    0.14278633
## 4                     0.15559988                    0.17624513
## 5                     0.05092447                    0.07640066
## 6                     0.22176827                    0.34301087
##   upper.975_q_clay_skill_winner upper.975_q_grass_skill_winner
## 1                    0.01330298                      0.1926295
## 2                    0.07627192                      0.1693405
## 3                    0.20041498                      0.2850858
## 4                    0.38578992                      0.3487652
## 5                    0.18364938                      0.2152060
## 6                    0.59344837                      0.4057635
##   upper.975_q_hard_skill_winner full_name_loser_loser
## 1                     0.1155232         Roger Federer
## 2                     0.1184587          Rafael Nadal
## 3                     0.2447351        Novak Djokovic
## 4                     0.2971484         Roger Federer
## 5                     0.1894577         Dominic Thiem
## 6                     0.4348574       Richard Gasquet
##   posterior_mean_clay_skill_loser posterior_mean_grass_skill_loser
## 1                       0.5782374                        0.5640599
## 2                       0.8923698                        0.4611610
## 3                       0.7241137                        0.6124707
## 4                       0.5445195                        0.5574316
## 5                       0.2765454                        0.1097986
## 6                       0.3719237                        0.3115141
##   posterior_mean_hard_skill_loser posterior_sd_clay_skill_loser
## 1                       0.6374161                    0.04636647
## 2                       0.5639528                    0.04393686
## 3                       0.7299929                    0.03681982
## 4                       0.6240920                    0.03863745
## 5                       0.1464562                    0.04440012
## 6                       0.3103122                    0.03971519
##   posterior_sd_grass_skill_loser posterior_sd_hard_skill_loser
## 1                     0.04963280                    0.03068106
## 2                     0.06461534                    0.03466660
## 3                     0.04407514                    0.02378226
## 4                     0.03970180                    0.02401464
## 5                     0.05750566                    0.04115824
## 6                     0.04486434                    0.02447069
##   posterior_median_clay_skill_loser posterior_median_grass_skill_loser
## 1                         0.5771920                          0.5646250
## 2                         0.8924285                          0.4597028
## 3                         0.7247434                          0.6121175
## 4                         0.5453214                          0.5565989
## 5                         0.2747548                          0.1118374
## 6                         0.3729132                          0.3099894
##   posterior_median_hard_skill_loser lower.025_q_clay_skill_loser
## 1                         0.6383055                    0.4877186
## 2                         0.5655935                    0.8079951
## 3                         0.7298320                    0.6525234
## 4                         0.6242605                    0.4692601
## 5                         0.1469190                    0.1891092
## 6                         0.3104455                    0.2953211
##   lower.025_q_grass_skill_loser lower.025_q_hard_skill_loser
## 1                   0.467068525                   0.57803980
## 2                   0.336212600                   0.49603785
## 3                   0.522193975                   0.68567258
## 4                   0.479590150                   0.57725560
## 5                  -0.002281075                   0.06577901
## 6                   0.228371903                   0.26231672
##   upper.975_q_clay_skill_loser upper.975_q_grass_skill_loser
## 1                    0.6731985                     0.6602861
## 2                    0.9753649                     0.5943746
## 3                    0.7954394                     0.6953446
## 4                    0.6209378                     0.6370795
## 5                    0.3648839                     0.2204306
## 6                    0.4516356                     0.4026846
##   upper.975_q_hard_skill_loser
## 1                    0.6968319
## 2                    0.6258220
## 3                    0.7796431
## 4                    0.6715561
## 5                    0.2239004
## 6                    0.3581013
head(multi_norm_games_model_bets)
##   winner_id loser_id                    score set_order winner_y  n winner_age
## 1    104660   103819 6-7(5) 7-6(5) 7-5 7-6(5)      0111       27 51   27.46338
## 2    104327   104745        7-6(4) 7-6(8) 6-4       111       20 36   29.28131
## 3    105023   104925    7-6(6) 6-1 3-6 7-6(5)      1101       23 42   28.72279
## 4    103333   105777           6-4 7-5 7-6(4)       111       20 35   35.23888
## 5    104898   104527              6-3 3-6 6-3       101       15 27   27.92334
## 6    104534   105062        7-6(5) 6-3 7-6(4)       111       20 35   30.13826
##   loser_age N_months_since_last_match_winner N_months_since_last_match_loser
## 1  31.87680                                0                               0
## 2  27.05818                                0                               0
## 3  29.10062                                0                               0
## 4  23.02806                                0                               0
## 5  29.94661                                0                               0
## 6  27.41136                                2                               0
##   surface tourney_date      month winner_rank loser_rank pp_p1_set_win_prob
## 1       3   2013-06-24 2013-06-01         116          3          0.1976539
## 2       3   2013-06-24 2013-06-01         135          5          0.2377964
## 3       3   2016-06-27 2016-06-01          41          1          0.2335658
## 4       2   2014-05-26 2014-05-01          37         12          0.3336490
## 5       1   2015-03-12 2015-03-01         104          7          0.2861232
## 6       2   2015-05-24 2015-05-01          91         58          0.2675205
##   pp_p1_match_win_prob pp_p1_y                model year  full_name_winner
## 1           0.06008175      25 Multi-Norm_bin_games 2013 Sergiy Stakhovsky
## 2           0.09706819      26 Multi-Norm_bin_games 2013      Steve Darcis
## 3           0.08922521      26 Multi-Norm_bin_games 2016       Sam Querrey
## 4           0.21716044      29 Multi-Norm_bin_games 2014      Ivo Karlovic
## 5           0.19965404      16 Multi-Norm_bin_games 2015       Robin Haase
## 6           0.12994293      27 Multi-Norm_bin_games 2015         Dudi Sela
##     full_name_loser          score2  MaxW MaxL  AvgW AvgL
## 1     Roger Federer 6-7 7-6 7-5 7-6 61.00 1.01 22.96 1.01
## 2      Rafael Nadal     7-6 7-6 6-4 46.00 1.02 20.68 1.01
## 3    Novak Djokovic 7-6 6-1 3-6 7-6 39.75 1.02 20.78 1.01
## 4   Grigor Dimitrov     6-4 7-5 7-6 10.50 1.10  7.81 1.08
## 5     Stan Wawrinka     6-3 3-6 6-3 10.50 1.08  8.42 1.06
## 6 Mikhail Kukushkin     7-6 6-3 7-6 10.15 1.14  7.57 1.08
##   best_winner_exp_payout best_loser_exp_payout avg_winner_exp_payout
## 1              2.6649865          -0.050682563            0.37947688
## 2              3.4651368          -0.079009555            1.00737019
## 3              2.5467023          -0.071009719            0.85409996
## 4              1.2801846          -0.138876482            0.69602303
## 5              1.0963675          -0.135626367            0.68108705
## 6              0.3189207          -0.008134937           -0.01633204
##   avg_loser_exp_payout max_exp_payout avg_exp_payout best_odds_profit
## 1          -0.05068256      2.6649865     0.37947688            60.00
## 2          -0.08803887      3.4651368     1.00737019            45.00
## 3          -0.08011747      2.5467023     0.85409996            38.75
## 4          -0.15453327      1.2801846     0.69602303             9.50
## 5          -0.15163329      1.0963675     0.68108705             9.50
## 6          -0.06033836      0.3189207    -0.01633204             9.15
##   full_name_winner_winner posterior_mean_clay_skill_winner
## 1       Sergiy Stakhovsky                      -0.10682459
## 2            Steve Darcis                      -0.07803581
## 3             Sam Querrey                       0.12240185
## 4            Ivo Karlovic                       0.04510460
## 5             Robin Haase                       0.13581067
## 6               Dudi Sela                      -0.23280174
##   posterior_mean_grass_skill_winner posterior_mean_hard_skill_winner
## 1                        0.08554668                      0.067709641
## 2                       -0.06147116                     -0.082394798
## 3                        0.23048449                      0.200340914
## 4                        0.20923892                      0.169590560
## 5                        0.02405439                      0.014069512
## 6                        0.06070916                     -0.009327006
##   posterior_sd_clay_skill_winner posterior_sd_grass_skill_winner
## 1                     0.06745985                      0.08006634
## 2                     0.09031717                      0.10077660
## 3                     0.05260695                      0.04832063
## 4                     0.07004510                      0.07183016
## 5                     0.05911125                      0.06606479
## 6                     0.08127090                      0.05979539
##   posterior_sd_hard_skill_winner posterior_median_clay_skill_winner
## 1                     0.04758902                        -0.10653500
## 2                     0.08374911                        -0.08012178
## 3                     0.03089251                         0.12178730
## 4                     0.04284108                         0.04326590
## 5                     0.04456762                         0.13490615
## 6                     0.04142017                        -0.23199205
##   posterior_median_grass_skill_winner posterior_median_hard_skill_winner
## 1                          0.08574315                         0.06791260
## 2                         -0.05980478                        -0.08109020
## 3                          0.22891860                         0.20066600
## 4                          0.20752918                         0.16944400
## 5                          0.02084311                         0.01330600
## 6                          0.06115216                        -0.00830731
##   lower.025_q_clay_skill_winner lower.025_q_grass_skill_winner
## 1                   -0.24122265                    -0.07214325
## 2                   -0.25922600                    -0.26016831
## 3                    0.02519172                     0.13922471
## 4                   -0.08873340                     0.07278720
## 5                    0.02045502                    -0.09876616
## 6                   -0.39979879                    -0.05427125
##   lower.025_q_hard_skill_winner upper.975_q_clay_skill_winner
## 1                   -0.02576766                    0.02232758
## 2                   -0.24539515                    0.09641766
## 3                    0.14007410                    0.22179742
## 4                    0.08721968                    0.18739390
## 5                   -0.07255006                    0.25626838
## 6                   -0.09044540                   -0.07746616
##   upper.975_q_grass_skill_winner upper.975_q_hard_skill_winner
## 1                      0.2430140                    0.16110207
## 2                      0.1403159                    0.07749756
## 3                      0.3297498                    0.25947965
## 4                      0.3543714                    0.25318442
## 5                      0.1625611                    0.10182585
## 6                      0.1816683                    0.06800549
##   full_name_loser_loser posterior_mean_clay_skill_loser
## 1         Roger Federer                      0.58075627
## 2          Rafael Nadal                      0.83900652
## 3        Novak Djokovic                      0.68400912
## 4       Grigor Dimitrov                      0.00885231
## 5         Stan Wawrinka                      0.33620289
## 6     Mikhail Kukushkin                     -0.04598250
##   posterior_mean_grass_skill_loser posterior_mean_hard_skill_loser
## 1                       0.53609416                      0.61973258
## 2                       0.46549165                      0.55265853
## 3                       0.59627543                      0.69661011
## 4                       0.11349168                      0.09619574
## 5                       0.23705304                      0.29860642
## 6                       0.01572389                      0.02052231
##   posterior_sd_clay_skill_loser posterior_sd_grass_skill_loser
## 1                    0.05639436                     0.06483414
## 2                    0.05491178                     0.07262470
## 3                    0.04479313                     0.05112788
## 4                    0.08810323                     0.08102545
## 5                    0.04302091                     0.06036466
## 6                    0.06298781                     0.06997370
##   posterior_sd_hard_skill_loser posterior_median_clay_skill_loser
## 1                    0.03874547                        0.58193790
## 2                    0.03808659                        0.83969650
## 3                    0.02877483                        0.68347275
## 4                    0.05893546                        0.00867405
## 5                    0.03501735                        0.33559445
## 6                    0.04884237                       -0.04585375
##   posterior_median_grass_skill_loser posterior_median_hard_skill_loser
## 1                         0.53486495                        0.62045450
## 2                         0.46271450                        0.55129850
## 3                         0.59566600                        0.69664900
## 4                         0.11208715                        0.09731970
## 5                         0.23694545                        0.29811050
## 6                         0.01669815                        0.02205305
##   lower.025_q_clay_skill_loser lower.025_q_grass_skill_loser
## 1                    0.4661212                    0.41093537
## 2                    0.7339556                    0.32628930
## 3                    0.5991965                    0.49639000
## 4                   -0.1700018                   -0.05032961
## 5                    0.2503511                    0.11527510
## 6                   -0.1645176                   -0.12806816
##   lower.025_q_hard_skill_loser upper.975_q_clay_skill_loser
## 1                   0.54256915                   0.68899397
## 2                   0.48211603                   0.95334970
## 3                   0.63931500                   0.77167489
## 4                  -0.01722189                   0.18685052
## 5                   0.23002267                   0.42111105
## 6                  -0.07423350                   0.07343379
##   upper.975_q_grass_skill_loser upper.975_q_hard_skill_loser
## 1                     0.6652784                    0.6932434
## 2                     0.6069289                    0.6277055
## 3                     0.6937463                    0.7526389
## 4                     0.2706805                    0.2082982
## 5                     0.3527775                    0.3665404
## 6                     0.1538255                    0.1155421
multi_norm_games_model_bets %>%
  group_by(surface) %>%
  summarize(profit = sum(best_odds_profit), n_bets_won = sum(best_odds_profit > 0), n_bets_placed = n())
## # A tibble: 3 × 4
##   surface profit n_bets_won n_bets_placed
##     <dbl>  <dbl>      <int>         <int>
## 1       1  -76.4        475          1235
## 2       2  -39.7        242           627
## 3       3  138.          96           264
multi_t_games_model_bets %>%
  group_by(surface) %>%
  summarize(profit = sum(best_odds_profit), n_bets_won = sum(best_odds_profit > 0), n_bets_placed = n())
## # A tibble: 3 × 4
##   surface profit n_bets_won n_bets_placed
##     <dbl>  <dbl>      <int>         <int>
## 1       1  -28.2          1            34
## 2       2  -11.1          3            30
## 3       3  133.           6            38
multi_norm_games_model_bets %>%
  filter(best_odds_profit > 0) %>%
  arrange(desc(best_odds_profit))
##     winner_id loser_id                          score set_order winner_y  n
## 1      104660   103819       6-7(5) 7-6(5) 7-5 7-6(5)      0111       27 51
## 2      104327   104745              7-6(4) 7-6(8) 6-4       111       20 36
## 3      105023   104925          7-6(6) 6-1 3-6 7-6(5)      1101       23 42
## 4      103333   105777                 6-4 7-5 7-6(4)       111       20 35
## 5      104898   104527                    6-3 3-6 6-3       101       15 27
## 6      104534   105062              7-6(5) 6-3 7-6(4)       111       20 35
## 7      104527   104925            2-6 6-4 6-2 3-6 9-7     01101       26 51
## 8      105332   105453         6-4 3-6 4-6 7-6(6) 6-4     10011       26 52
## 9      103781   106233                        6-3 7-5        11       13 21
## 10     103285   104918                    7-6(10) 6-2        11       13 21
## 11     103970   104745                     7-6(1) 6-4        11       13 23
## 12     103970   104755                6-3 6-4 5-7 6-2      1101       23 39
## 13     104947   105668          7-6(4) 6-4 6-7(4) 6-3      1101       25 45
## 14     103970   104745                        6-3 7-5        11       13 21
## 15     104620   104259            4-6 6-4 6-3 2-6 7-5     01101       25 49
## 16     104468   104918                        6-4 6-2        11       12 18
## 17     104269   104745                    6-4 2-6 6-3       101       14 27
## 18     104122   103970                        6-3 6-3        11       12 18
## 19     104542   104925                        6-2 6-2        11       12 16
## 20     105992   105777                    7-5 4-6 6-0       101       17 28
## 21     105373   105453                 7-6(4) 6-1 6-2       111       19 28
## 22     104594   105227                        6-4 6-4        11       12 20
## 23     105575   105683                    6-3 4-6 6-3       101       16 28
## 24     104424   105238                 5-7 7-6(5) 6-3       011       18 34
## 25     104330   104545              6-7(5) 6-3 7-6(8)       011       19 35
## 26     104586   105138                    6-4 6-2 6-2       111       18 26
## 27     104330   104926                    6-1 6-2 6-2       111       18 23
## 28     104527   104745                6-3 6-2 3-6 6-3      1101       21 35
## 29     104268   104259                 5-7 7-6(5) 6-4       011       18 35
## 30     104678   105683                        6-4 6-4        11       12 20
## 31     105385   104731                     6-2 7-6(6)        11       13 21
## 32     103888   104678                        6-2 6-2        11       12 16
## 33     104471   104545                 6-4 6-7(4) 6-3       101       18 32
## 34     104719   104792              7-6(6) 6-7(7) 6-4       101       19 36
## 35     103852   105453                     6-4 7-6(2)        11       13 23
## 36     103163   104527                    5-7 6-2 6-3       011       17 29
## 37     104620   105683                 6-4 3-6 7-6(3)       101       16 32
## 38     105062   105777         6-3 7-6(2) 2-6 4-6 6-4     11001       25 50
## 39     104586   104926                        6-3 6-2        11       12 17
## 40     104559   104660             6-7(3) 6-4 6-2 6-0      0111       24 37
## 41     104731   104527                 7-6(1) 4-6 6-1       101       17 30
## 42     105217   104731                        6-4 7-5        11       13 22
## 43     105332   105453                    1-6 6-4 6-2       011       13 25
## 44     104122   104607                    0-6 7-5 6-1       011       13 25
## 45     103970   104918                    2-6 6-1 6-2       011       14 23
## 46     104792   103819                     6-4 7-6(5)        11       13 23
## 47     105238   104745                 6-3 6-7(6) 6-4       101       18 32
## 48     105053   104597                        7-5 6-3        11       13 21
## 49     104460   104545              6-4 6-7(7) 7-6(4)       101       19 36
## 50     103781   105227                 6-2 6-7(5) 6-3       101       18 30
## 51     104898   104755                        6-4 6-4        11       12 20
## 52     105379   104871                    3-6 6-2 6-1       011       15 24
## 53     103917   105023                 7-5 7-6(6) 7-5       111       21 37
## 54     103794   105777                     6-4 7-6(3)        11       13 23
## 55     105332   105676                        6-2 6-3        11       12 17
## 56     103819   104925                    3-6 6-3 6-2       011       15 26
## 57     104468   103970                6-3 3-6 6-1 6-3      1011       21 34
## 58     103333   105227                 7-5 2-6 7-6(2)       101       16 33
## 59     103188   103720                     6-3 7-6(6)        11       13 22
## 60     105077   105023                    4-6 6-3 6-4       011       16 29
## 61     104594   104545                        6-4 6-4        11       12 20
## 62     104594   104259                        6-2 6-2        11       12 16
## 63     105238   104607                        6-4 6-2        11       12 18
## 64     105668   105777                    6-4 3-6 6-3       101       15 28
## 65     103898   104542                        6-4 6-4        11       12 20
## 66     104918   105683              6-4 7-6(3) 7-6(2)       111       20 36
## 67     104022   104468                        6-1 6-4        11       12 17
## 68     104312   103720         7-6(4) 6-3 5-7 5-7 7-5     11001       30 58
## 69     105379   105138                 3-6 6-3 7-6(8)       011       16 31
## 70     104468   105227      4-6 7-6(3) 6-7(5) 6-1 6-2     01011       29 51
## 71     104719   105238            1-6 3-6 6-3 6-0 6-2     00111       22 39
## 72     103852   105683                 6-4 6-7(5) 6-3       101       18 32
## 73     105575   104468                        6-4 6-2        11       12 18
## 74     104338   104755                     7-6(7) 6-4        11       13 23
## 75     104947   103852                    3-6 7-5 6-3       011       16 30
## 76     105332   104926                    6-1 6-3 7-5       111       19 28
## 77     104678   103970                        6-3 6-4        11       12 19
## 78     104620   105577            2-6 6-4 6-2 3-6 6-3     01101       23 44
## 79     104022   104542                        6-1 6-4        11       12 17
## 80     102967   104468                     7-6(4) 6-3        11       13 22
## 81     105373   104597                     6-4 7-6(3)        11       13 23
## 82     105041   104797                    5-7 6-1 6-4       011       17 29
## 83     104180   105777                     6-2 7-6(8)        11       13 21
## 84     105147   105449                        6-4 6-4        11       12 20
## 85     105643   104527                 6-7(5) 6-4 6-4       011       18 33
## 86     105668   104792                        6-4 7-5        11       13 22
## 87     105208   104545                    6-4 4-6 6-4       101       16 30
## 88     103997   104731                     7-6(3) 6-4        11       13 23
## 89     103898   105777                        7-5 6-3        11       13 21
## 90     103997   104559                        6-3 7-5        11       13 21
## 91     105373   104926                    2-6 6-1 6-2       011       14 23
## 92     104586   104259                     7-5 7-6(5)        11       14 25
## 93     103819   104925                        7-5 6-2        11       13 20
## 94     104559   104545                     6-2 7-6(2)        11       13 21
## 95     104918   104925                    6-4 4-6 6-3       101       16 29
## 96     104269   104542                    4-6 6-3 6-4       011       16 29
## 97     104424   105173                        6-2 6-4        11       12 18
## 98     104122   105683                        7-5 6-4        11       13 22
## 99     103333   104607                 7-5 6-7(8) 6-3       101       19 34
## 100    104291   104660                     7-6(2) 6-4        11       13 23
## 101    104542   105453            6-1 6-4 4-6 3-6 6-3     11001       25 45
## 102    103898   104527                    1-6 6-1 6-2       011       13 22
## 103    104571   103970                     6-2 7-6(4)        11       13 21
## 104    104468   104607                 7-6(4) 4-6 6-0       101       17 29
## 105    103917   103990                     6-1 7-6(0)        11       13 20
## 106    105577   104678         4-6 6-7(4) 6-4 6-3 6-3     00111       28 51
## 107    103819   104925                        7-5 6-2        11       13 20
## 108    105062   103990                 3-6 6-3 7-6(4)       011       16 31
## 109    104665   103990                        6-1 6-1        11       12 14
## 110    103893   104665                        6-2 6-0        11       12 14
## 111    104468   105683                    4-6 6-3 7-5       011       17 31
## 112    104897   104919              7-6(3) 6-7(4) 6-3       101       19 35
## 113    104180   106071                 7-6(3) 7-6(13)        11       14 26
## 114    105332   104259                    6-3 3-6 6-1       101       15 25
## 115    103812   104731                        6-4 6-4        11       12 20
## 116    104919   104312         6-3 2-6 4-6 7-6(5) 6-4     10011       25 50
## 117    104735   105238                    7-5 2-6 7-5       101       16 32
## 118    103898   105208                     7-6(4) 6-3        11       13 22
## 119    103819   104925                        6-4 6-4        11       12 20
## 120    103794   104871                    5-7 6-1 7-5       011       18 31
## 121    103898   105208                    6-4 4-6 7-5       101       17 32
## 122    104660   105208                 6-4 6-3 7-6(5)       111       19 32
## 123    103852   105683                     7-6(4) 6-4        11       13 23
## 124    104022   104678                        6-3 7-5        11       13 21
## 125    105575   103781              7-6(5) 3-6 7-6(6)       101       17 35
## 126    104620   105676                        6-3 6-3        11       12 18
## 127    104545   105453                        6-4 6-3        11       12 19
## 128    104252   104022                     7-6(8) 6-4        11       13 23
## 129    105064   105138                    1-6 6-1 6-4       011       13 24
## 130    105053   105227                        7-5 6-3        11       13 21
## 131    103781   105173              7-6(5) 6-3 7-6(4)       111       20 35
## 132    104180   105777                     6-4 7-6(5)        11       13 23
## 133    104947   105723                        6-1 6-2        11       12 15
## 134    104542   104745                    6-4 0-6 7-5       101       13 28
## 135    105053   103990                        6-3 6-4        11       12 19
## 136    104731   104527                 7-6(4) 7-6(11)        11       14 26
## 137    104719   104471                 7-6(8) 4-6 6-3       101       17 32
## 138    104269   104755                     7-6(5) 6-1        11       13 20
## 139    105238   104527                    6-4 3-6 6-1       101       15 26
## 140    103813   104098                  7-6(3) 7-6(3)        11       14 26
## 141    104338   104252                    6-1 6-2 6-4       111       18 25
## 142    105449   104731                 5-7 7-6(5) 6-4       011       18 35
## 143    104312   103285                 7-6(8) 4-6 6-4       101       17 33
## 144    105238   106210                     6-3 7-6(6)        11       13 22
## 145    106071   104755                 6-3 6-7(1) 6-4       101       18 32
## 146    104678   106058                        6-2 6-3        11       12 17
## 147    104571   104259              3-6 7-6(1) 7-6(5)       011       17 35
## 148    105051   105173                    6-3 4-6 6-3       101       16 28
## 149    104068   104660                 7-6(3) 3-6 6-0       101       16 28
## 150    104731   104527                     7-6(8) 7-5        11       14 25
## 151    104424   104897                     7-6(4) 7-5        11       14 25
## 152    103990   105777                    6-4 1-6 7-5       101       14 29
## 153    104719   105373          6-7(5) 6-2 7-6(4) 7-5      0111       26 46
## 154    104919   104259                        7-5 6-4        11       13 22
## 155    104460   105023                    6-2 4-6 6-4       101       16 28
## 156    105332   104655                        6-4 6-3        11       12 19
## 157    103781   104926             6-7(5) 7-5 6-3 6-2      0111       25 42
## 158    104919   103990                 3-6 7-6(8) 6-4       011       16 32
## 159    104898   104022                    3-6 6-1 6-4       011       15 26
## 160    104559   105053             6-3 1-6 7-6(6) 6-3      1011       20 38
## 161    105311   104180                     7-6(9) 6-3        11       13 22
## 162    103843   105332              7-6(3) 2-6 7-6(4)       101       16 34
## 163    103794   105992                 7-5 3-6 7-6(2)       101       17 34
## 164    105137   103893                     7-6(3) 6-3        11       13 22
## 165    104871   104731                        6-4 6-4        11       12 20
## 166    104665   104259         6-1 7-6(5) 3-6 3-6 6-4     11001       25 48
## 167    104542   104607             6-3 6-2 6-7(5) 6-3      1101       24 39
## 168    104291   105064                        6-3 6-2        11       12 17
## 169    103819   104925                        6-3 7-5        11       13 21
## 170    103451   104534                        6-4 6-3        11       12 19
## 171    103794   103333                     7-6(5) 6-4        11       13 23
## 172    104571   105676                6-1 6-4 4-6 6-0      1101       22 33
## 173    104660   104471              7-6(6) 6-7(4) 6-2       101       19 34
## 174    104719   103917          6-4 7-6(6) 6-7(7) 6-4      1101       25 46
## 175    104291   105385                        7-5 6-4        11       13 22
## 176    103285   104471                5-7 6-3 6-4 6-1      0111       23 38
## 177    104731   105453                 7-6(10) 7-6(3)        11       14 26
## 178    104291   104559                        7-5 6-4        11       13 22
## 179    104468   104978       6-7(4) 6-4 3-6 6-3 16-14     01011       37 71
## 180    103656   105053                     7-6(1) 7-5        11       14 25
## 181    103781   105992                     7-6(3) 6-3        11       13 22
## 182    104338   105227                        6-4 6-4        11       12 20
## 183    104586   104098                     6-4 7-6(4)        11       13 23
## 184    103656   105238                     7-6(5) 6-3        11       13 22
## 185    105173   104926                    6-3 6-4 6-1       111       18 26
## 186    105238   104468                        6-0 6-3        11       12 15
## 187    105373   103990                     7-6(5) 6-4        11       13 23
## 188    104655   105777                        6-2 6-4        11       12 18
## 189    105011   105311                     6-3 7-6(2)        11       13 22
## 190    104797   105023                  7-6(1) 7-6(6)        11       14 26
## 191    104926   105449             2-6 6-3 6-4 7-6(2)      0111       21 40
## 192    103781   106045                    6-3 7-5 6-1       111       19 28
## 193    104797   105062                 7-6(4) 2-6 6-2       101       15 29
## 194    103333   105683                  7-6(1) 7-6(1)        11       14 26
## 195    103990   105227                    7-6(10) 6-3        11       13 22
## 196    103898   103720                        6-1 6-2        11       12 15
## 197    104882   105385                    7-5 6-4 6-4       111       19 32
## 198    104571   104327                        6-4 6-2        11       12 18
## 199    104349   105311                     7-6(5) 6-3        11       13 22
## 200    103656   104898                     6-1 7-6(4)        11       13 20
## 201    104898   105332                    6-4 2-6 6-2       101       14 26
## 202    104180   104871                 2-6 7-6(1) 6-4       011       15 31
## 203    105227   104542                     6-3 7-6(5)        11       13 22
## 204    105208   105238                    7-5 4-6 6-1       101       17 29
## 205    103565   104308          7-6(3) 6-1 6-7(3) 6-1      1101       25 40
## 206    105023   105208                    6-2 6-3 6-4       111       18 27
## 207    103970   104607                        6-4 7-5        11       13 22
## 208    103786   103898                     7-6(6) 7-5        11       14 25
## 209    104269   104468                    6-3 3-6 6-4       101       15 28
## 210    103852   105138                     7-6(7) 6-3        11       13 22
## 211    103970   105453                        6-3 7-5        11       13 21
## 212    105575   105449                        6-4 6-2        11       12 18
## 213    104731   105238                    6-1 5-7 6-4       101       17 29
## 214    103163   105453                     7-6(3) 6-2        11       13 21
## 215    105332   103656                    6-4 5-7 6-4       101       17 32
## 216    104534   105173                        6-3 6-1        11       12 16
## 217    104797   106071                     6-4 7-6(6)        11       13 23
## 218    104312   104871                7-5 3-6 6-2 6-1      1011       22 36
## 219    104180   105676              7-6(5) 6-7(6) 6-3       101       19 35
## 220    104871   104545                6-4 4-6 6-3 6-3      1011       22 38
## 221    104755   104527           6-4 4-6 3-6 6-4 11-9     10011       30 59
## 222    105332   104180                  7-6(5) 7-6(6)        11       14 26
## 223    103794   104979                    6-4 1-6 6-4       101       13 27
## 224    104898   104122                 6-2 6-7(4) 6-2       101       18 29
## 225    104312   105053                    6-3 7-5 6-3       111       19 30
## 226    105668   104468                        6-2 7-5        11       13 20
## 227    104166   105992                    6-3 2-6 6-2       101       14 25
## 228    104312   104252                    4-6 6-1 7-5       011       17 29
## 229    104268   103813                        6-2 6-1        11       12 15
## 230    104545   103990      7-6(13) 7-6(3) 6-7(5) 7-5      1101       27 51
## 231    103898   105208                        6-4 6-4        11       12 20
## 232    104022   105208                        6-4 6-1        11       12 17
## 233    105683   105453           6-7(4) 7-6(4) 7-6(4)       011       20 39
## 234    105575   104180                 3-6 7-6(5) 6-4       011       16 32
## 235    105373   105064                    5-7 6-3 7-5       011       18 33
## 236    104586   105373                    4-6 6-0 6-3       011       16 25
## 237    104338   104597                 6-3 6-7(6) 6-4       101       18 32
## 238    104269   104597                     6-3 7-6(4)        11       13 22
## 239    104268   105154                 6-7(3) 6-1 6-4       011       18 30
## 240    103333   104545                  7-6(4) 7-6(5)        11       14 26
## 241    104745   104918                        6-4 6-1        11       12 17
## 242    104620   104594                        6-3 6-2        11       12 17
## 243    103898   105577                     7-6(3) 6-3        11       13 22
## 244    105064   104655                    2-6 6-2 7-5       011       15 28
## 245    104460   105723                        6-2 6-4        11       12 18
## 246    104660   104678                        6-4 6-2        11       12 18
## 247    105138   104755                        6-4 6-1        11       12 17
## 248    105208   103333                  7-6(4) 7-6(5)        11       14 26
## 249    103813   104898                        6-3 6-2        11       12 17
## 250    103852   105023                        6-4 6-4        11       12 20
## 251    105238   104926                        6-1 6-1        11       12 14
## 252    104547   104655                 7-6(3) 3-6 6-3       101       16 31
## 253    104898   104022                        6-3 6-3        11       12 18
## 254    103781   104269           7-6(3) 6-7(6) 7-6(9)       101       20 39
## 255    104291   105575                        7-5 6-3        11       13 21
## 256    104665   104926                        6-1 6-3        11       12 16
## 257    105373   105577                     6-4 7-6(7)        11       13 23
## 258    103781   104545                     7-6(7) 6-3        11       13 22
## 259    105227   104542                        6-4 6-4        11       12 20
## 260    105668   105676                        6-4 6-2        11       12 18
## 261    104468   104792                 6-4 1-6 7-6(4)       101       14 30
## 262    104755   104597                     6-1 7-6(4)        11       13 20
## 263    104259   103990                        6-2 6-4        11       12 18
## 264    104259   104545       7-6(4) 4-6 7-6(2) 7-6(4)      1011       25 49
## 265    104312   104620                        6-4 6-3        11       12 19
## 266    103188   104308                    3-6 6-3 6-1       011       15 25
## 267    104586   104978                     7-6(4) 6-4        11       13 23
## 268    103565   104166                        7-5 6-4        11       13 22
## 269    104655   104871                        6-2 6-2        11       12 16
## 270    103852   105668              7-6(6) 6-4 7-6(3)       111       20 36
## 271    104545   105683           6-7(3) 7-6(6) 7-6(5)       011       20 39
## 272    104871   105676                    6-3 6-4 6-2       111       18 27
## 273    105023   104545                     6-3 7-6(3)        11       13 22
## 274    105539   104559                        6-3 6-2        11       12 17
## 275    105449   106058                     7-6(5) 6-1        11       13 20
## 276    104534   104586                     6-3 7-6(2)        11       13 22
## 277    103285   104797                    6-1 3-6 6-1       101       15 23
## 278    104871   104586                    4-6 6-3 6-4       011       16 29
## 279    103898   104468                        6-3 6-4        11       12 19
## 280    104338   105577                    7-5 2-6 6-3       101       15 29
## 281    104571   103333              3-6 7-6(5) 7-6(7)       011       17 35
## 282    105208   104660                     6-4 7-6(3)        11       13 23
## 283    104327   105173                     7-6(4) 6-4        11       13 23
## 284    104999   104926                     6-2 7-6(3)        11       13 21
## 285    105668   105138                    6-4 1-6 6-4       101       13 27
## 286    105208   105777                     6-4 7-6(3)        11       13 23
## 287    103917   104882                        6-3 6-2        11       12 17
## 288    103917   105138                        6-2 6-4        11       12 18
## 289    103401   104268           7-6(5) 6-7(6) 7-6(7)       101       20 39
## 290    103333   106071              3-6 7-6(5) 7-6(6)       011       17 35
## 291    105227   104542         6-4 6-4 3-6 6-7(3) 6-4     11001       27 52
## 292    105023   105238                     7-6(5) 6-4        11       13 23
## 293    104918   105453                        6-3 6-4        11       12 19
## 294    104098   104797                     7-6(5) 6-2        11       13 21
## 295    105062   104433                    6-3 6-3 6-2       111       18 26
## 296    104797   105668                        6-1 6-1        11       12 14
## 297    105385   105173                     6-3 7-6(9)        11       13 22
## 298    104660   104719                     6-2 7-6(7)        11       13 21
## 299    104594   104719                        6-4 6-2        11       12 18
## 300    104122   104926                        6-3 6-0        11       12 15
## 301    104327   104180                 6-4 6-7(2) 6-3       101       18 32
## 302    104719   105173                        6-3 6-0        11       12 15
## 303    105238   106071                        6-4 6-1        11       12 17
## 304    104534   105332                     6-4 7-6(2)        11       13 23
## 305    104534   105385                        6-3 6-0        11       12 15
## 306    104997   105173                 7-6(3) 4-6 6-1       101       17 30
## 307    104792   104259                    7-5 3-6 6-3       101       16 30
## 308    105577   104926                6-3 6-4 1-6 6-3      1101       19 35
## 309    104898   104655                    6-2 5-7 6-1       101       17 27
## 310    105064   104471                     7-6(0) 6-4        11       13 23
## 311    105053   104898                    6-2 3-6 6-0       101       15 23
## 312    104665   104719                        6-3 6-0        11       12 15
## 313    103794   105041                        6-3 6-2        11       12 17
## 314    105077   104919                        6-2 6-0        11       12 14
## 315    105227   103990              7-5 6-7(3) 7-6(5)       101       20 38
## 316    104312   105077                        6-3 6-4        11       12 19
## 317    104268   104898                     7-6(1) 6-4        11       13 23
## 318    104468   106071                        6-3 6-2        11       12 17
## 319    104979   104559                        6-3 6-3        11       12 18
## 320    104719   103565                    6-3 6-4 6-4       111       18 29
## 321    104527   105453                 6-3 6-4 7-6(6)       111       19 32
## 322    104460   104594                        6-4 6-4        11       12 20
## 323    104545   105777                     7-6(2) 6-2        11       13 21
## 324    105023   104468                 5-7 7-6(8) 6-4       011       18 35
## 325    104571   104180                 7-6(5) 4-6 6-3       101       17 32
## 326    104312   103794                        6-1 6-2        11       12 15
## 327    105332   104797                        6-4 6-2        11       12 18
## 328    104571   104180              6-7(4) 6-3 7-6(4)       011       19 35
## 329    104545   105208                  7-6(4) 7-6(3)        11       14 26
## 330    103656   104308                 5-7 7-6(5) 6-3       011       18 34
## 331    103285   104665                    5-7 6-3 6-4       011       17 31
## 332    103333   104735                 3-6 7-5 7-6(5)       011       17 34
## 333    103812   104665                        6-4 6-4        11       12 20
## 334    104898   103852                 4-6 7-6(2) 6-4       011       17 33
## 335    104571   106071                     7-6(7) 6-3        11       13 22
## 336    104559   105051                    2-6 6-3 6-2       011       14 25
## 337    105023   104731                     7-6(4) 6-4        11       13 23
## 338    104542   104926                    5-7 6-3 6-0       011       17 27
## 339    104792   105777                 7-5 7-6(6) 7-5       111       21 37
## 340    103188   105385                    4-6 6-1 6-2       011       16 25
## 341    105575   105041                        6-0 6-2        11       12 14
## 342    104386   106071                 5-7 6-1 7-6(3)       011       18 32
## 343    106210   105373                        6-3 6-4        11       12 19
## 344    104755   105777                    6-3 6-4 6-4       111       18 29
## 345    104545   104259           6-7(4) 7-6(4) 7-6(5)       011       20 39
## 346    104252   104471                        6-3 6-2        11       12 17
## 347    105683   103990                        6-4 6-3        11       12 19
## 348    104022   104919                        6-1 6-1        11       12 14
## 349    103917   104978                        7-5 6-3        11       13 21
## 350    104269   104755                    6-3 6-2 6-3       111       18 26
## 351    105332   104979                 1-6 6-1 7-6(4)       011       14 27
## 352    104534   103794                    6-3 3-6 6-3       101       15 27
## 353    104607   105227                        6-3 6-1        11       12 16
## 354    104678   103852                 6-7(7) 7-5 6-4       011       19 35
## 355    104607   104542                        6-3 6-4        11       12 19
## 356    104678   103852                 6-7(2) 6-4 6-3       011       18 32
## 357    103917   105676                     7-6(1) 6-1        11       13 20
## 358    104545   103852           7-6(5) 6-7(9) 7-6(4)       101       20 39
## 359    104797   105385                        6-3 6-3        11       12 18
## 360    104571   105023                     7-6(2) 6-1        11       13 20
## 361    104797   104098             7-6(3) 4-6 6-1 6-4      1011       23 40
## 362    104897   105173                    4-6 6-1 6-4       011       16 27
## 363    104338   104919                        6-4 6-4        11       12 20
## 364    103333   103852                     7-6(2) 6-4        11       13 23
## 365    104338   105077                 7-6(4) 2-6 7-5       101       16 33
## 366    104871   104594   6-7(5) 7-6(7) 7-6(9) 4-6 7-5     01101       31 61
## 367    104735   104620                    3-6 6-3 6-4       011       15 28
## 368    104678   104620                    7-5 3-6 6-4       101       16 31
## 369    104312   105373                        6-2 6-4        11       12 18
## 370    104597   103813                 3-6 7-6(6) 6-4       011       16 32
## 371    104022   104660                        6-2 6-1        11       12 15
## 372    104871   104471                        6-3 6-2        11       12 17
## 373    104755   105453                        6-1 6-4        11       12 17
## 374    104312   104919              5-7 7-6(4) 7-6(4)       011       19 38
## 375    104312   105173                        6-3 6-3        11       12 18
## 376    104947   105147                        6-3 6-4        11       12 19
## 377    104468   104122                        6-4 6-1        11       12 17
## 378    104571   103333                 7-6(5) 6-4 6-4       111       19 33
## 379    104252   103656                    4-6 6-2 6-2       011       16 26
## 380    103917   105992                     7-6(2) 7-5        11       14 25
## 381    105053   104719                  7-6(7) 7-6(2)        11       14 26
## 382    105064   105053                    3-6 6-4 6-3       011       15 28
## 383    105373   104719                        6-4 6-3        11       12 19
## 384    104571   105053                    1-6 6-2 7-5       011       14 27
## 385    105453   105777                     7-6(1) 7-5        11       14 25
## 386    104792   104926            5-7 6-2 6-4 0-6 6-2     01101       23 44
## 387    105373   105385                     7-6(4) 6-4        11       13 23
## 388    104997   104979                     7-6(5) 6-3        11       13 22
## 389    104269   103813                        6-3 6-4        11       12 19
## 390    103990   105577                 6-3 4-6 7-6(5)       101       17 32
## 391    104678   105062                        6-2 6-3        11       12 17
## 392    104534   104586             7-6(2) 5-7 7-5 6-3      1011       25 46
## 393    104338   104655              7-6(1) 6-7(4) 6-4       101       19 36
## 394    103781   104932                 6-4 6-7(5) 6-3       101       18 32
## 395    105668   104460                 6-7(5) 6-4 6-3       011       18 32
## 396    103333   105238       5-7 6-3 6-4 6-7(4) 13-11     01101       36 68
## 397    104597   104269                    6-4 1-6 7-5       101       14 29
## 398    103813   104897                 7-6(4) 7-5 7-5       111       21 37
## 399    105575   104559                        7-5 6-4        11       13 22
## 400    104534   105041                        6-3 6-2        11       12 17
## 401    104947   105173                        6-4 6-1        11       12 17
## 402    105575   105311         6-2 6-2 4-6 2-6 7-6(4)     11001       25 47
## 403    104460   104559                 4-6 6-1 7-6(1)       011       17 30
## 404    103781   105062                 7-6(5) 3-6 6-3       101       16 31
## 405    103163   104312                    6-1 4-6 6-3       101       16 26
## 406    105053   103794                     6-2 7-6(3)        11       13 21
## 407    105227   105453                    6-3 6-3 6-3       111       18 27
## 408    104269   105138                 3-6 7-5 7-6(4)       011       17 34
## 409    104898   104268                6-2 3-6 6-4 6-2      1011       21 35
## 410    103163   104871                        6-3 6-4        11       12 19
## 411    105208   105238                        6-3 6-4        11       12 19
## 412    103813   104919                     7-6(5) 6-4        11       13 23
## 413    103813   104947                        6-3 6-4        11       12 19
## 414    104797   104494                    4-6 6-0 6-3       011       16 25
## 415    103720   104594                        6-4 6-3        11       12 19
## 416    104665   104719                        7-5 6-3        11       13 21
## 417    103812   103565                    7-5 3-6 6-4       101       16 31
## 418    104586   103566                        6-4 6-4        11       12 20
## 419    104918   104597                    6-1 1-6 6-4       101       13 24
## 420    104542   105238                     6-3 7-6(5)        11       13 22
## 421    103656   104919                 6-7(6) 6-4 6-4       011       18 33
## 422    103794   105577              6-7(3) 7-6(5) 6-4       011       19 36
## 423    103656   104216                    4-6 6-4 6-0       011       16 26
## 424    104607   104792                        6-1 6-4        11       12 17
## 425    105023   105238                    4-6 6-3 7-5       011       17 31
## 426    104925   103819         7-6(1) 6-7(10) 6-4 6-3      1011       25 45
## 427    104571   105208                    6-4 4-6 6-3       101       16 29
## 428    103333   104871                     6-4 7-6(6)        11       13 23
## 429    105683   105453             4-6 6-1 7-6(4) 6-3      0111       23 39
## 430    103990   104586      6-1 6-7(7) 3-6 7-6(5) 8-6     10011       30 56
## 431    103819   103813                        6-2 7-5        11       13 20
## 432    104180   103893      4-6 4-6 7-6(1) 7-6(5) 6-4     00111       28 56
## 433    103656   105332                    7-5 4-6 6-2       101       17 30
## 434    103813   104559                        6-4 6-4        11       12 20
## 435    103333   104978              6-7(4) 7-5 7-6(3)       011       20 38
## 436    105077   103813                        6-2 7-5        11       13 20
## 437    104468   103812                    2-6 6-3 6-3       011       14 26
## 438    105023   103898                     7-6(5) 6-4        11       13 23
## 439    104269   104594                    6-3 3-6 6-3       101       15 27
## 440    104542   105676                        6-3 6-4        11       12 19
## 441    104792   105777                        6-1 6-3        11       12 16
## 442    104545   105577                 7-6(1) 4-6 6-3       101       17 32
## 443    104678   105373                        6-2 6-3        11       12 17
## 444    104678   104620                    6-3 3-6 7-5       101       16 30
## 445    104312   105053                    4-6 6-2 7-5       011       17 30
## 446    103819   104918                        6-3 7-5        11       13 21
## 447    104460   104330                    6-3 3-6 6-3       101       15 27
## 448    103813   103794                        7-5 6-4        11       13 22
## 449    103813   105217                     7-6(3) 6-4        11       13 23
## 450    103813   105053                 6-3 6-7(5) 6-3       101       18 31
## 451    104259   104871                    6-3 4-6 6-4       101       16 29
## 452    105373   104327         3-6 2-6 7-6(5) 7-5 6-4     00111       25 52
## 453    104678   104180                        6-2 6-4        11       12 18
## 454    104291   105147                        7-5 6-1        11       13 19
## 455    103852   104926                 6-3 7-6(5) 6-1       111       19 29
## 456    105577   104620                        6-3 6-4        11       12 19
## 457    104731   106058                     6-3 7-6(7)        11       13 22
## 458    105023   104871           6-7(4) 7-6(4) 7-6(5)       011       20 39
## 459    104022   104338                    5-7 6-3 6-2       011       17 29
## 460    104269   105385                    4-6 6-1 6-3       011       16 26
## 461    105208   105385                        6-4 6-4        11       12 20
## 462    104745   104527                        6-2 6-1        11       12 15
## 463    104797   104534                     7-6(1) 6-2        11       13 21
## 464    105041   105051                7-6(10) 5-7 6-4       101       18 35
## 465    105138   105577                 7-6(1) 3-6 6-4       101       16 32
## 466    103813   104978                    4-6 6-2 6-2       011       16 26
## 467    104755   104731                        6-3 6-4        11       12 19
## 468    103285   104731                    1-6 6-3 6-2       011       13 24
## 469    104542   105777                        6-4 6-3        11       12 19
## 470    105064   104559                        6-4 6-4        11       12 20
## 471    104997   104433                        6-4 7-5        11       13 22
## 472    104797   104919              6-3 6-7(8) 7-6(6)       101       19 35
## 473    104022   104471              7-6(7) 6-7(4) 6-3       101       19 35
## 474    106071   104926                        6-3 6-2        11       12 17
## 475    104597   106210                 6-7(2) 7-5 6-4       011       19 35
## 476    104542   104731                 7-6(6) 5-7 6-4       101       18 35
## 477    103990   105173                 6-4 6-1 7-6(5)       111       19 30
## 478    105668   104559                        6-4 6-4        11       12 20
## 479    104918   105227                        6-1 6-4        11       12 17
## 480    104312   104655                        7-5 6-3        11       13 21
## 481    104678   106071           7-6(3) 6-7(4) 7-6(4)       101       20 39
## 482    104468   105676                 6-7(6) 7-5 6-2       011       19 33
## 483    104571   105577                     6-4 7-6(5)        11       13 23
## 484    104269   105077                        6-1 7-5        11       13 19
## 485    104259   104926                     7-6(0) 6-4        11       13 23
## 486    104545   104559                     7-6(8) 6-4        11       13 23
## 487    103781   104268                        6-4 6-3        11       12 19
## 488    104534   104308                     6-1 7-6(2)        11       13 20
## 489    104338   104312                    6-2 3-6 6-3       101       15 26
## 490    103794   104882                     6-3 7-6(7)        11       13 22
## 491    104918   104542                    7-5 7-5 6-4       111       20 34
## 492    104607   105777                    5-7 6-4 6-4       011       17 32
## 493    104678   104919                6-4 4-6 6-4 6-0      1011       22 36
## 494    104534   105132                        6-3 6-4        11       12 19
## 495    104755   105138                 6-4 3-6 7-6(6)       101       16 32
## 496    104597   104660                 6-3 6-7(3) 6-4       101       18 32
## 497    105227   104545 7-6(4) 6-7(6) 6-4 6-7(4) 12-10     10101       37 71
## 498    103990   104312                    6-3 1-6 6-4       101       13 26
## 499    103656   105575                    1-6 6-4 7-5       011       14 29
## 500    104745   105227                    4-6 6-3 6-3       011       16 28
## 501    104755   106071                    6-4 3-6 6-3       101       15 28
## 502    103852   104655                    6-2 4-6 6-3       101       16 27
## 503    104338   105643      6-7(4) 6-2 6-1 6-7(6) 6-2     01101       30 49
## 504    103898   105051                        6-2 6-2        11       12 16
## 505    103819   104607                    3-6 6-4 6-3       011       15 28
## 506    103852   104871                        6-3 6-4        11       12 19
## 507    104571   104460             6-4 7-5 2-6 7-6(4)      1101       22 43
## 508    104338   105064                     7-6(1) 6-1        11       13 20
## 509    103333   105385                        6-3 6-3        11       12 18
## 510    104571   104586                        6-3 6-4        11       12 19
## 511    104571   104620                        6-4 6-4        11       12 20
## 512    104745   104527                        6-3 6-2        11       12 17
## 513    105668   104586                        6-3 6-2        11       12 17
## 514    104925   103819                6-4 5-7 6-4 6-4      1011       23 42
## 515    104678   104655                    2-6 6-4 6-4       011       14 28
## 516    104919   104559                6-2 4-6 6-4 6-4      1011       22 38
## 517    104745   104925                3-6 7-5 6-2 6-4      0111       22 39
## 518    104918   104607             6-7(6) 6-0 6-3 7-5      0111       25 40
## 519    104898   105575                 6-3 6-7(6) 6-4       101       18 32
## 520    105208   104586                    6-2 5-7 6-3       101       17 29
## 521    104468   104180                        6-4 6-4        11       12 20
## 522    104925   104745                        6-3 6-3        11       12 18
## 523    105777   105577                        6-2 6-2        11       12 16
## 524    104918   103970                        6-4 7-5        11       13 22
## 525    104022   104882                    6-3 1-6 6-4       101       13 26
## 526    104597   103990                     6-3 7-6(1)        11       13 22
## 527    103990   104620                    1-6 6-2 6-4       011       13 25
## 528    104607   105777                    3-6 6-3 6-2       011       15 26
## 529    104918   104269                 6-4 7-5 7-6(3)       111       20 35
## 530    105668   105173                 2-6 7-6(5) 6-4       011       15 31
## 531    105053   103401                    6-3 6-2 6-2       111       18 25
## 532    104918   105453                        6-3 6-0        11       12 15
## 533    103794   105147                        6-3 6-3        11       12 18
## 534    104755   104122                 7-6(5) 6-4 6-4       111       19 33
## 535    104022   104312                        6-3 6-4        11       12 19
## 536    104259   103794                     6-4 7-6(3)        11       13 23
## 537    106071   105173                    3-6 6-4 6-4       011       15 29
## 538    104471   105311                        6-3 7-5        11       13 21
## 539    104259   104660                        6-2 7-5        11       13 20
## 540    104122   103898                    6-1 4-6 6-3       101       16 26
## 541    104731   104926                        7-5 6-2        11       13 20
## 542    104792   105138                        6-4 6-1        11       12 17
## 543    105676   104620              7-6(5) 6-7(4) 6-1       101       19 33
## 544    104755   103333              6-4 6-7(2) 7-6(6)       101       19 36
## 545    104098   104586                    3-6 6-3 6-3       011       15 27
## 546    104338   103781                        6-4 6-3        11       12 19
## 547    104468   104898                 7-6(1) 6-4 6-4       111       19 33
## 548    104678   104979                        6-3 6-4        11       12 19
## 549    103970   104545                 6-3 6-7(6) 6-2       101       18 30
## 550    104607   104468                        6-3 6-3        11       12 18
## 551    104471   104655                        7-5 6-2        11       13 20
## 552    104269   104919                    6-4 3-6 6-3       101       15 28
## 553    104022   104979                    4-6 6-2 6-3       011       16 27
## 554    104586   104660                        7-5 6-2        11       13 20
## 555    105227   104919                    6-3 6-2 6-4       111       18 27
## 556    103819   104542                    6-3 7-5 6-4       111       19 31
## 557    104678   104586                        6-3 6-2        11       12 17
## 558    105683   105138                     7-5 7-6(7)        11       14 25
## 559    103333   105173                        6-3 6-4        11       12 19
## 560    105373   104665                     7-6(4) 6-3        11       13 22
## 561    103970   104755                        6-4 7-5        11       13 22
## 562    104745   106071                 6-4 6-7(6) 6-3       101       18 32
## 563    104898   104797                    3-6 6-1 6-3       011       15 25
## 564    103333   103794                        6-4 6-4        11       12 20
## 565    103813   104979                 6-1 6-2 7-6(6)       111       19 28
## 566    104597   105238             6-3 2-6 6-4 7-6(6)      1011       21 40
## 567    103786   103997            3-6 6-3 3-6 6-3 6-4     01011       24 46
## 568    105077   103835                        6-2 6-1        11       12 15
## 569    105023   104660                     7-6(2) 6-3        11       13 22
## 570    104338   104719                        6-1 6-2        11       12 15
## 571    104338   103812                        6-4 7-5        11       13 22
## 572    104527   104731                    6-4 6-4 6-0       111       18 26
## 573    104745   105683                     6-3 7-6(3)        11       13 22
## 574    103794   105385                    6-4 6-3 6-4       111       18 29
## 575    104338   105311                     6-2 7-6(4)        11       13 21
## 576    105227   103990                        6-3 6-3        11       12 18
## 577    103333   104460                 6-3 6-7(3) 6-2       101       18 30
## 578    105575   104291                        6-4 6-4        11       12 20
## 579    105227   104471                        7-5 6-4        11       13 22
## 580    105992   103451                        6-3 6-4        11       12 19
## 581    104571   104330                        6-3 6-4        11       12 19
## 582    103970   103990                    6-4 3-6 6-3       101       15 28
## 583    105668   104268                    6-2 5-7 6-2       101       17 28
## 584    104926   105379                        6-4 7-5        11       13 22
## 585    104660   105011             6-4 7-6(2) 4-6 6-4      1101       23 43
## 586    104607   105777                        7-5 6-4        11       13 22
## 587    104269   104678                 6-4 6-7(7) 6-1       101       18 30
## 588    104755   105577                        7-5 7-5        11       14 24
## 589    104468   105311                        6-4 6-1        11       12 17
## 590    104527   103333           6-7(2) 7-6(5) 7-6(5)       011       20 39
## 591    103566   105041                     6-3 7-6(2)        11       13 22
## 592    103898   104655                 6-3 6-7(3) 6-4       101       18 32
## 593    103970   105676                    6-3 2-6 6-3       101       14 26
## 594    104460   103893                     7-6(3) 6-3        11       13 22
## 595    105064   104797                     7-6(4) 6-3        11       13 22
## 596    103852   104999                     6-3 7-6(4)        11       13 22
## 597    104607   105208                        6-3 6-2        11       12 17
## 598    104269   105053                        6-4 7-5        11       13 22
## 599    104269   104719                 5-7 6-3 7-6(5)       011       18 34
## 600    104665   103893                    3-6 6-0 6-3       011       15 24
## 601    104918   104792            6-4 6-1 4-6 1-6 6-0     11001       23 40
## 602    104468   104180                 4-6 7-6(1) 6-3       011       17 32
## 603    105643   105723                        6-3 6-4        11       12 19
## 604    103786   104979                     7-6(6) 6-4        11       13 23
## 605    104122   104559                        6-4 6-1        11       12 17
## 606    104918   105777                        6-3 6-3        11       12 18
## 607    104918   105683                        6-3 7-5        11       13 21
## 608    105023   103794                    4-6 6-2 6-1       011       16 25
## 609    104259   104268                        6-1 6-4        11       12 17
## 610    103970   103852                        7-5 7-5        11       14 24
## 611    103333   105051                        7-5 6-4        11       13 22
## 612    103970   104259           6-7(4) 7-6(4) 7-6(4)       011       20 39
## 613    104312   104216                     7-6(3) 6-2        11       13 21
## 614    104755   104180                        6-3 6-2        11       12 17
## 615    104527   105676                        7-5 6-3        11       13 21
## 616    104571   104559         6-2 6-7(5) 3-6 6-4 6-4     10011       27 50
## 617    104542   106071                     7-6(7) 6-3        11       13 22
## 618    104259   104898                        6-2 6-4        11       12 18
## 619    104269   106045                        6-4 6-4        11       12 20
## 620    104259   104797                    6-2 4-6 6-4       101       16 28
## 621    104471   104559                        6-2 6-2        11       12 16
## 622    103819   105453                     6-3 7-6(4)        11       13 22
## 623    103333   104586                     7-6(4) 6-3        11       13 22
## 624    104338   104559                    6-2 3-6 6-3       101       15 26
## 625    105227   104871             6-3 2-6 7-6(2) 6-1      1011       21 37
## 626    105777   105311                    2-6 6-3 6-4       011       14 27
## 627    104607   106058                     7-6(1) 6-2        11       13 21
## 628    105238   104926                        6-2 6-4        11       12 18
## 629    103720   105992                    1-6 7-5 6-4       011       14 29
## 630    103970   105373                 4-6 7-6(4) 6-4       011       17 33
## 631    103333   104586                     7-6(4) 6-3        11       13 22
## 632    104731   105385                    4-6 6-3 6-4       011       16 29
## 633    104745   106058                    3-6 6-4 6-3       011       15 28
## 634    104745   104926                        7-5 6-3        11       13 21
## 635    104745   105777                    6-4 4-6 6-3       101       16 29
## 636    103819   105453                        6-3 6-2        11       12 17
## 637    104542   105023                     7-6(6) 6-0        11       13 19
## 638    104571   105385                5-7 6-2 6-4 6-4      0111       23 40
## 639    105053   105311                    6-3 3-6 6-1       101       15 25
## 640    104542   104180      7-6(8) 6-7(3) 6-4 3-6 6-2     10101       28 53
## 641    104755   104180                     7-6(4) 6-2        11       13 21
## 642    103163   103794                    4-6 6-3 6-3       011       16 28
## 643    104597   104871                     7-6(7) 6-3        11       13 22
## 644    103970   105208                     7-6(3) 6-3        11       13 22
## 645    104468   103835                        6-2 6-3        11       12 17
## 646    105577   103893                    6-3 3-6 6-3       101       15 27
## 647    105227   103852                        6-3 6-4        11       12 19
## 648    103819   105683                        6-2 6-3        11       12 17
## 649    104122   105550                     6-4 7-6(4)        11       13 23
## 650    105238   104559                     7-6(4) 6-3        11       13 22
## 651    104597   104919                     7-6(4) 6-2        11       13 21
## 652    105053   104297                        7-5 6-2        11       13 20
## 653    104745   103333              7-5 6-7(4) 7-6(4)       101       20 38
## 654    104731   104926                     6-3 7-6(1)        11       13 22
## 655    104918   104259          3-6 6-3 6-3 4-6 12-10     01101       31 59
## 656    104527   103990             7-5 4-6 7-6(7) 6-2      1011       24 43
## 657    104797   104308                     6-4 7-6(5)        11       13 23
## 658    105208   104559                        6-1 6-4        11       12 17
## 659    104338   103813                        6-3 6-4        11       12 19
## 660    104918   104545              6-7(3) 6-4 7-6(2)       011       19 36
## 661    104259   105723                     7-6(1) 6-3        11       13 22
## 662    104338   104547                        6-3 6-1        11       12 16
## 663    103163   104268                        6-2 6-4        11       12 18
## 664    103819   105683                    6-4 6-4 6-4       111       18 30
## 665    103970   103333                     7-6(5) 6-4        11       13 23
## 666    104269   104559                 4-6 6-3 7-6(4)       011       17 32
## 667    104678   104665                    4-6 6-3 6-3       011       16 28
## 668    105023   105053             6-3 6-2 3-6 7-6(3)      1101       22 39
## 669    104607   103852                        6-1 6-2        11       12 15
## 670    104607   104926                 6-3 3-6 7-6(2)       101       16 31
## 671    104312   104559             3-6 6-3 7-6(3) 6-1      0111       22 38
## 672    103285   103188                    5-7 6-3 6-1       011       17 28
## 673    105138   105173                    7-5 6-2 6-3       111       19 29
## 674    103990   104665                     7-6(4) 6-4        11       13 23
## 675    103970   103333           6-7(2) 7-6(5) 7-6(4)       011       20 39
## 676    104468   105311                    5-7 6-3 6-2       011       17 29
## 677    104338   103813                     6-1 7-6(4)        11       13 20
## 678    104918   104755                    4-6 6-1 6-4       011       16 27
## 679    105227   105449                        6-3 6-3        11       12 18
## 680    104792   104327                    4-6 6-2 6-3       011       16 27
## 681    103970   105777                        6-4 6-2        11       12 18
## 682    104269   104655         4-6 6-7(6) 7-5 6-4 6-3     00111       29 54
## 683    104792   105311                        6-1 6-4        11       12 17
## 684    104269   103893                        6-1 6-2        11       12 15
## 685    104678   105011              4-6 7-6(3) 7-6(3)       011       18 36
## 686    104745   103970                    6-4 5-7 6-2       101       17 30
## 687    104542   104586                        7-5 6-3        11       13 21
## 688    104678   104330            7-6(10) 6-4 3-6 6-3      1101       22 41
## 689    104755   104534                        6-3 6-2        11       12 17
## 690    104665   105173                 3-6 7-6(2) 6-2       011       16 30
## 691    104755   104620                        6-1 6-2        11       12 15
## 692    103990   104665                    3-6 6-3 6-1       011       15 25
## 693    105227   105385                    7-5 5-7 6-4       101       18 34
## 694    103970   104871                 6-2 7-6(5) 6-2       111       19 29
## 695    103970   104926                        6-4 6-3        11       12 19
## 696    103970   105208                        6-2 6-3        11       12 17
## 697    104731   103565                    7-5 6-3 6-4       111       19 31
## 698    104338   104979                    0-6 6-2 6-1       011       12 21
## 699    103970   104471                    1-6 6-3 6-3       011       13 25
## 700    103819   104792                    6-4 4-6 6-3       101       16 29
## 701    103970   103898                        6-3 6-2        11       12 17
## 702    104792   104620                        6-4 6-4        11       12 20
## 703    103970   106071                    6-4 3-6 6-1       101       15 26
## 704    104269   104559                        6-2 6-3        11       12 17
## 705    105208   104997                 6-4 6-4 7-6(3)       111       19 33
## 706    105208   104947                        6-2 6-0        11       12 14
## 707    105138   104559                    6-3 5-7 7-5       101       18 33
## 708    104607   106058                 7-6(3) 4-6 6-4       101       17 33
## 709    103819   104792                6-3 4-6 6-4 6-1      1011       22 36
## 710    104259   104620                        6-3 6-4        11       12 19
## 711    104755   105373                        6-3 6-4        11       12 19
## 712    103819   105683                     6-1 7-6(0)        11       13 20
## 713    103333   105147                  7-6(5) 7-6(3)        11       14 26
## 714    105643   104297                    1-6 6-4 6-4       011       13 27
## 715    104269   105385                     7-6(1) 6-1        11       13 20
## 716    104918   104719                        6-2 7-5        11       13 20
## 717    104918   103898                        6-3 6-4        11       12 19
## 718    104607   106071                 6-2 7-6(3) 6-2       111       19 29
## 719    104792   104586                 6-7(3) 6-3 6-3       011       18 31
## 720    104259   104797                 6-3 7-6(5) 6-2       111       19 30
## 721    105227   105062                    4-6 6-3 6-2       011       16 27
## 722    104755   103333                        6-3 6-4        11       12 19
## 723    103970   105227                    6-2 6-2 6-4       111       18 26
## 724    104542   105332                    6-4 6-3 6-4       111       18 29
## 725    104468   105385                        6-4 6-3        11       12 19
## 726    103163   104547                    6-3 5-7 6-2       101       17 29
## 727    103786   104534                        6-3 6-1        11       12 16
## 728    103819   104527             3-6 7-6(5) 6-4 6-4      0111       22 42
## 729    104269   104216                        6-2 6-3        11       12 17
## 730    104745   104607                     7-6(3) 6-1        11       13 20
## 731    103819   105238                        6-3 6-1        11       12 16
## 732    104745   104731                 4-6 7-6(6) 6-2       011       17 31
## 733    104745   104731                    7-5 6-1 6-4       111       19 29
## 734    104122   105011            4-6 3-6 6-3 7-5 6-2     00111       26 48
## 735    103819   104527                    6-4 6-3 6-1       111       18 26
## 736    103163   104639                        6-2 6-1        11       12 15
## 737    104338   103794                        6-2 6-1        11       12 15
## 738    104269   103566              6-2 7-6(4) 7-6(3)       111       20 34
## 739    104527   104594                        7-5 6-3        11       13 21
## 740    104918   103990                 5-7 7-6(9) 6-1       011       18 32
## 741    104338   103893                    6-3 5-7 6-3       101       17 30
## 742    104755   104620                        6-3 6-2        11       12 17
## 743    104259   104586                 7-6(4) 6-2 6-2       111       19 29
## 744    103970   105062                        6-3 6-4        11       12 19
## 745    103970   104545                        6-4 6-4        11       12 20
## 746    104925   105777          6-4 3-6 7-6(2) 7-6(7)      1011       23 45
## 747    103819   105777                        6-2 6-2        11       12 16
## 748    104918   105777             6-4 6-7(5) 6-3 7-5      1011       25 44
## 749    103819   104655                    6-3 7-6(11)        11       13 22
## 750    104022   103794                        6-3 6-4        11       12 19
## 751    104338   105137                        6-3 6-1        11       12 16
## 752    104745   104871                        6-3 6-4        11       12 19
## 753    104925   104527                        6-4 6-1        11       12 17
## 754    104269   104547                        7-5 7-5        11       14 24
## 755    104755   106071                    6-2 6-1 7-5       111       19 27
## 756    103819   104792            4-6 3-6 6-4 7-5 6-2     00111       26 49
## 757    104745   104620                        6-2 6-2        11       12 16
## 758    104925   104527         7-6(1) 3-6 6-4 4-6 6-0     10101       26 48
## 759    103970   104926                        6-2 6-3        11       12 17
## 760    104745   105577                     7-6(3) 6-4        11       13 23
## 761    104745   105777                        6-2 6-2        11       12 16
## 762    104312   105173                        6-2 6-1        11       12 15
## 763    104918   103990              3-6 7-6(7) 7-6(8)       011       17 35
## 764    105227   105723                        6-2 6-1        11       12 15
## 765    103970   104926                        6-4 6-2        11       12 18
## 766    104022   104308                        6-3 6-4        11       12 19
## 767    103819   104468                  7-6(6) 7-6(2)        11       14 26
## 768    103819   105777                     7-6(4) 6-2        11       13 21
## 769    104755   104665                        6-3 7-5        11       13 21
## 770    105227   104999              4-6 7-6(5) 7-6(5)       011       18 36
## 771    105227   105311                        6-4 6-2        11       12 18
## 772    104607   105373                        6-4 6-1        11       12 17
## 773    105053   104297                        6-2 6-2        11       12 16
## 774    104545   104665                 7-6(5) 1-6 6-3       101       14 29
## 775    104925   105453                        6-2 6-3        11       12 17
## 776    104925   105777                        6-2 6-4        11       12 18
## 777    103819   105676                        6-2 6-2        11       12 16
## 778    104925   104545                 7-5 6-7(2) 6-1       101       19 32
## 779    103970   104665                        6-0 6-2        11       12 14
## 780    103819   103852                        6-3 6-4        11       12 19
## 781    104269   104424                 6-3 6-2 7-6(3)       111       19 30
## 782    105683   105311                     6-3 7-6(4)        11       13 22
## 783    104745   105777                        6-3 6-4        11       12 19
## 784    104918   103852                        6-4 6-1        11       12 17
## 785    103819   103898                     7-6(4) 6-0        11       13 19
## 786    104918   105577                        6-4 6-4        11       12 20
## 787    104745   104926                        7-5 7-5        11       14 24
## 788    104745   105238                     6-3 7-6(3)        11       13 22
## 789    104745   104918                    6-3 6-2 6-1       111       18 24
## 790    104542   104499                    6-2 6-2 7-5       111       19 28
## 791    103819   105138                        6-4 6-2        11       12 18
## 792    104607   105173                 6-4 6-7(3) 6-2       101       18 31
## 793    104745   104586                        6-2 6-2        11       12 16
## 794    104925   104545                     7-6(3) 6-2        11       13 21
## 795    104745   104655                        6-3 6-2        11       12 17
## 796    104527   105311                     7-6(1) 7-5        11       14 25
## 797    104745   104545                        6-4 6-4        11       12 20
## 798    104745   104269                    3-6 6-1 6-1       011       15 23
## 799    104745   104586                 1-6 7-5 7-6(4)       011       15 32
## 800    104918   103852                 7-6(2) 6-4 6-2       111       19 31
## 801    104925   105208                6-3 6-3 3-6 6-3      1101       21 36
## 802    103819   105577                 7-6(4) 5-7 6-2       101       18 33
## 803    104745   105385                        6-4 6-2        11       12 18
## 804    104745   104545                 7-6(6) 4-6 6-3       101       17 32
## 805    104607   104559                    6-3 6-2 6-4       111       18 27
## 806    104918   104926                        6-2 6-4        11       12 18
## 807    104745   104338                        6-4 6-1        11       12 17
## 808    104918   104665                    3-6 6-1 6-2       011       15 24
## 809    104745   104534                    6-1 6-0 7-5       111       19 25
## 810    103819   104586                        6-2 6-2        11       12 16
## 811    104745   104122                     7-6(7) 6-2        11       13 21
## 812    104745   104312                        6-1 6-2        11       12 15
## 813    104918   104897                    6-3 6-3 6-4       111       18 28
##     winner_age loser_age N_months_since_last_match_winner
## 1     27.46338  31.87680                                0
## 2     29.28131  27.05818                                0
## 3     28.72279  29.10062                                0
## 4     35.23888  23.02806                                0
## 5     27.92334  29.94661                                0
## 6     30.13826  27.41136                                2
## 7     28.79671  26.64750                                0
## 8     26.31348  25.67009                                0
## 9     35.15674  22.87201                                0
## 10    35.53183  27.06913                                0
## 11    32.03285  27.86311                                0
## 12    35.25257  31.04175                                0
## 13    28.04928  24.62423                                0
## 14    31.57290  27.40315                                0
## 15    28.70637  30.68583                                0
## 16    30.11910  27.73990                                0
## 17    31.35113  28.80219                                0
## 18    31.42231  32.26283                                0
## 19    29.29774  27.20329                                0
## 20    22.79808  23.77550                                0
## 21    24.87337  24.40520                                0
## 22    28.83504  25.69473                                0
## 23    24.31211  23.79466                                0
## 24    30.88843  26.71595                                0
## 25    31.31828  30.21218                                9
## 26    29.83436  27.11020                                0
## 27    29.44011  26.25873                                0
## 28    28.79671  27.61396                                0
## 29    30.56810  30.64750                                0
## 30    29.64819  24.77207                                0
## 31    26.25873  29.44011                                0
## 32    33.68652  29.51403                                0
## 33    29.58522  29.27310                                2
## 34    29.05955  28.67077                                0
## 35    33.46475  25.19097                                0
## 36    36.10678  29.12252                                0
## 37    29.35797  24.13963                                0
## 38    27.67967  24.29295                                0
## 39    28.79945  26.96783                                0
## 40    28.64339  28.01916                                2
## 41    27.79192  28.93087                                0
## 42    25.83436  28.17522                                0
## 43    26.40931  25.76591                                0
## 44    31.23066  28.61054                                0
## 45    32.51198  27.39493                                0
## 46    28.61328  33.67830                                0
## 47    26.60096  29.03217                                0
## 48    26.39836  28.66530                                0
## 49    29.32786  28.94730                                0
## 50    32.97194  25.61807                                0
## 51    27.17591  27.97536                                0
## 52    26.27242  28.70089                                0
## 53    33.60712  27.89870                                0
## 54    34.28337  24.36961                                0
## 55    26.19849  24.61602                                0
## 56    32.54757  26.76249                                0
## 57    29.65914  32.39699                                0
## 58    35.60301  26.02053                                0
## 59    35.78097  32.96099                                0
## 60    25.97125  26.25051                                0
## 61    29.52498  29.80972                                0
## 62    28.73922  30.55168                                0
## 63    26.77344  29.91376                                0
## 64    23.74264  23.23888                                0
## 65    32.19986  28.87611                                0
## 66    29.11978  25.50034                                0
## 67    33.12526  30.61739                                0
## 68    29.89459  32.88433                                0
## 69    25.46749  26.72690                                0
## 70    29.04586  25.29227                                0
## 71    28.12047  25.54689                                0
## 72    32.87064  23.60301                                0
## 73    24.25462  29.73580                                0
## 74    30.48323  28.26283                                0
## 75    27.70431  33.42642                                0
## 76    26.04517  28.00274                                0
## 77    28.61328  32.47365                                0
## 78    28.87885  24.17248                                2
## 79    32.12868  29.31691                                0
## 80    36.84873  29.10335                                0
## 81    25.73580  29.62355                                0
## 82    26.71321  27.86858                                0
## 83    31.75633  23.73717                                0
## 84    27.15127  25.54962                                0
## 85    24.61602  30.13826                                0
## 86    24.75838  28.95825                                0
## 87    27.13484  30.48049                                0
## 88    32.64066  28.63518                                6
## 89    32.79398  23.39220                                0
## 90    31.95072  28.93087                                0
## 91    24.79671  26.92950                                0
## 92    28.95277  30.72416                                0
## 93    34.27242  28.48734                                0
## 94    29.86995  29.94387                                0
## 95    28.23819  28.21903                                0
## 96    31.75359  30.33265                                0
## 97    30.88843  27.07461                                0
## 98    31.23066  23.33470                                0
## 99    36.29295  29.74127                                0
## 100   30.51882  28.55578                                0
## 101   30.10267  25.40178                                0
## 102   32.64066  29.37166                                0
## 103   30.01232  33.22108                                0
## 104   29.77413  29.05133                                0
## 105   32.57221  32.29843                                0
## 106   25.01574  29.37988                                0
## 107   32.68172  26.89665                                0
## 108   26.77892  32.43258                                0
## 109   28.06845  31.80014                                0
## 110   32.61602  28.50924                                0
## 111   30.46407  24.46543                                0
## 112   27.53183  27.41410                                0
## 113   31.67967  22.22587                                0
## 114   26.21766  31.77823                                0
## 115   32.71184  27.88775                                0
## 116   27.10746  30.33539                                0
## 117   28.14784  25.68104                                0
## 118   32.62149  25.92745                                0
## 119   33.16085  27.37577                                0
## 120   34.28337  28.62423                                0
## 121   32.23819  25.54415                                0
## 122   28.45996  25.81246                                0
## 123   33.90554  24.63792                                0
## 124   33.12526  29.49487                                0
## 125   23.85216  32.93361                                0
## 126   29.26215  24.09856                                0
## 127   29.90554  25.22930                                0
## 128   31.52088  32.79945                               12
## 129   27.36208  27.07187                                0
## 130   27.47159  26.63381                                0
## 131   34.00684  26.90212                                0
## 132   32.10130  24.08214                                0
## 133   28.12594  24.42437                                0
## 134   30.48597  29.35797                                0
## 135   26.36003  31.93429                                0
## 136   29.07598  30.21492                                0
## 137   28.81040  30.08350                                0
## 138   30.29706  27.70705                                0
## 139   25.35524  28.96920                                0
## 140   32.87885  31.49076                                0
## 141   31.24983  31.73169                                0
## 142   25.81793  29.42094                                0
## 143   30.06708  35.30185                                0
## 144   26.98426  22.31348                                0
## 145   22.97331  29.31691                                0
## 146   29.72485  23.10472                                0
## 147   28.74743  30.41752                                0
## 148   26.55441  25.96304                                0
## 149   31.78645  28.53662                                0
## 150   28.21355  29.35250                                0
## 151   30.40931  27.83847                                0
## 152   32.85421  23.81383                                0
## 153   28.12047  24.87337                                0
## 154   27.16496  30.74333                                0
## 155   30.59274  27.76454                                0
## 156   26.19849  29.54689                                0
## 157   32.09035  26.08624                                0
## 158   26.72416  31.76181                                0
## 159   27.29090  32.07118                                0
## 160   29.25667  26.74333                                0
## 161   26.57358  32.46543                                0
## 162   33.74127  26.08350                                7
## 163   32.75017  21.85900                                0
## 164   26.09446  32.40520                                2
## 165   27.62765  28.36687                                0
## 166   29.33333  31.60575                                0
## 167   30.10267  29.68378                                0
## 168   31.59206  27.64956                                0
## 169   33.54415  27.75907                                0
## 170   34.33539  28.83504                                0
## 171   33.15264  35.44969                                0
## 172   29.59069  24.11773                                0
## 173   28.13415  29.14442                                0
## 174   28.19713  32.41889                                0
## 175   30.71047  25.20465                                0
## 176   36.49008  30.39014                                0
## 177   29.40178  25.78508                                0
## 178   31.59206  30.25325                                0
## 179   29.04586  26.49418                                0
## 180   34.18480  27.18412                                0
## 181   33.83436  22.87474                                0
## 182   30.94319  26.44216                                0
## 183   28.58864  31.20329                                0
## 184   33.39904  25.45106                                0
## 185   26.15469  27.25530                                0
## 186   25.94935  29.81246                                0
## 187   25.77413  32.96920                                0
## 188   29.31691  23.94798                                0
## 189   27.74812  26.19028                                0
## 190   28.78850  27.70705                                0
## 191   28.27105  25.68378                                0
## 192   34.27515  23.03628                                0
## 193   29.03765  27.73717                                0
## 194   36.44627  24.61875                                0
## 195   32.22177  25.80972                                0
## 196   32.62149  33.44011                                0
## 197   27.47433  25.08966                                0
## 198   29.83984  31.10198                                0
## 199   31.04449  26.07529                                1
## 200   33.22656  26.86927                                0
## 201   27.36756  25.27858                                0
## 202   31.67967  27.91513                                0
## 203   26.53799  29.98768                                0
## 204   26.71321  26.52430                                0
## 205   33.65914  29.90828                                0
## 206   26.26968  25.37166                                0
## 207   32.76112  29.30048                                0
## 208   32.67351  32.12320                                0
## 209   30.94867  29.83162                                0
## 210   32.87064  26.30527                                0
## 211   32.89528  25.15264                                0
## 212   25.09788  25.58795                                0
## 213   27.77276  25.29774                                0
## 214   35.91513  24.17522                                0
## 215   24.91444  33.36071                                2
## 216   29.25667  26.02053                                0
## 217   27.88775  21.76591                                0
## 218   30.91034  27.93429                                0
## 219   31.75633  24.17522                                0
## 220   28.27926  30.07803                                0
## 221   29.02943  30.25325                                0
## 222   26.27515  32.27379                                0
## 223   34.26420  28.16701                                0
## 224   26.85010  31.01985                                0
## 225   30.25873  26.49418                                0
## 226   24.22177  30.09993                                0
## 227   30.80356  21.76318                                0
## 228   30.00958  30.39014                                0
## 229   30.45311  32.76386                                0
## 230   29.08145  32.06845                                0
## 231   32.75565  26.06160                                0
## 232   32.28200  26.09993                                0
## 233   24.02464  25.01848                                0
## 234   24.61875  31.73717                                0
## 235   25.58248  27.11294                                0
## 236   29.62355  25.65914                                0
## 237   30.90486  29.50856                                0
## 238   30.39288  28.62697                                0
## 239   31.21971  26.68583                                0
## 240   34.98973  28.83231                                0
## 241   29.45380  28.50650                                0
## 242   29.26215  29.42916                                0
## 243   33.06229  24.55578                                0
## 244   27.22793  29.22108                                0
## 245   30.32444  24.11773                                0
## 246   29.45654  29.36071                                0
## 247   27.47433  29.29774                                0
## 248   27.13484  36.63792                                0
## 249   32.78303  27.08008                                0
## 250   33.10062  27.05544                                0
## 251   25.27858  26.73785                                0
## 252   28.82957  28.14784                                0
## 253   27.04175  31.82204                                0
## 254   33.06776  30.58453                                0
## 255   30.46133  24.04381                                0
## 256   29.23751  27.90691                                0
## 257   26.19576  25.24572                                0
## 258   32.97194  29.04312                                0
## 259   25.36893  28.81862                                0
## 260   23.76181  23.69610                                0
## 261   30.13826  28.45996                                0
## 262   28.85695  29.68104                                0
## 263   30.57084  32.03012                                0
## 264   30.85832  29.33060                                0
## 265   30.58453  28.95551                                0
## 266   35.78097  29.98494                                0
## 267   28.58864  26.60917                                0
## 268   33.83162  30.89938                                0
## 269   28.51198  27.39767                                0
## 270   33.33060  24.18344                                0
## 271   29.90554  24.23546                                0
## 272   28.27926  24.46270                                0
## 273   27.86037  30.30801                                0
## 274   25.44559  30.40657                                0
## 275   25.60712  22.85558                                0
## 276   28.83504  28.53114                                0
## 277   35.26352  27.48528                                0
## 278   27.22519  28.78029                                0
## 279   32.48734  29.46749                                0
## 280   30.48323  24.24914                                0
## 281   29.62902  35.92882                                0
## 282   26.78987  29.43737                                0
## 283   31.60027  27.30459                                0
## 284   28.17796  28.42437                                0
## 285   24.35592  26.93771                                0
## 286   25.44832  22.74059                                0
## 287   32.57221  27.45517                                0
## 288   33.37714  27.14853                                0
## 289   36.01643  31.66051                                0
## 290   35.43053  21.78508                                0
## 291   26.92129  30.37098                                0
## 292   27.99452  26.90760                                1
## 293   27.96988  25.34428                                0
## 294   31.06913  27.33196                                0
## 295   26.49144  29.73854                                0
## 296   28.11773  23.93429                                0
## 297   25.54962  26.61465                                0
## 298   29.09240  28.82957                                0
## 299   29.54415  28.86790                                0
## 300   32.05476  27.75359                                0
## 301   31.02533  31.87132                                0
## 302   29.00205  26.78713                                0
## 303   26.77344  22.81999                                0
## 304   29.19918  25.10609                                0
## 305   29.29500  24.99384                                0
## 306   27.46064  26.59548                                0
## 307   28.76660  31.64408                                0
## 308   25.01574  28.09856                                0
## 309   28.53662  29.79603                                0
## 310   26.32717  29.31691                                0
## 311   27.31828  27.96167                                0
## 312   28.04928  27.83299                                0
## 313   32.65435  26.27242                                0
## 314   26.08624  26.76249                                0
## 315   25.56057  31.97262                                0
## 316   30.18207  26.27789                                0
## 317   30.56810  27.17591                                0
## 318   29.62081  21.80424                                0
## 319   27.24709  29.40999                                0
## 320   28.77207  34.67488                                0
## 321   29.81246  25.05681                                0
## 322   30.17112  29.50582                                0
## 323   29.90554  23.85216                                0
## 324   27.70705  30.48323                                0
## 325   30.33812  32.44627                                0
## 326   31.29363  33.97673                                0
## 327   26.19849  28.86516                                0
## 328   30.10815  32.21629                                0
## 329   28.85147  25.50582                                0
## 330   33.30322  30.08077                                0
## 331   35.45517  28.29843                                0
## 332   35.21971  27.99452                                0
## 333   32.96099  28.45175                                0
## 334   28.05749  33.59890                                0
## 335   30.33812  22.99247                                0
## 336   28.73922  26.22861                                0
## 337   26.86379  28.25188                                0
## 338   28.99110  26.89117                                0
## 339   27.98084  23.27721                                0
## 340   35.83847  24.61054                                0
## 341   24.61875  27.24983                                0
## 342   30.84463  22.51335                                0
## 343   22.12183  26.11910                                0
## 344   29.02943  24.12047                                0
## 345   28.69815  30.22587                                0
## 346   30.44764  29.20192                                0
## 347   23.29637  31.95346                                0
## 348   32.03285  27.14579                                0
## 349   32.05476  26.57084                                0
## 350   30.52704  27.93703                                0
## 351   25.18275  26.97878                                0
## 352   29.29500  33.09514                                0
## 353   29.14716  26.11636                                0
## 354   29.72485  34.11636                                0
## 355   30.12457  30.54346                                0
## 356   29.24572  33.63723                                0
## 357   33.37714  24.50103                                0
## 358   30.13552  33.73306                                0
## 359   28.96099  26.08624                                0
## 360   30.33812  28.03285                                0
## 361   27.35113  31.08830                                0
## 362   27.53183  26.28884                                0
## 363   30.90486  27.77823                                0
## 364   34.95140  32.39151                                0
## 365   29.90828  26.10541                                0
## 366   27.35934  28.87337                                0
## 367   28.39699  29.01300                                0
## 368   29.11157  29.45380                                0
## 369   31.42779  26.04244                                0
## 370   30.16016  34.23956                                0
## 371   32.60780  29.07324                                0
## 372   27.24435  29.35524                                0
## 373   28.10951  24.57769                                0
## 374   30.87201  27.64408                                2
## 375   31.48528  27.13210                                0
## 376   28.35592  27.41958                                1
## 377   29.39083  31.28816                                0
## 378   29.93566  36.23546                                0
## 379   31.80835  34.66393                                0
## 380   31.95893  21.66735                                0
## 381   26.18754  27.81383                                0
## 382   26.13552  26.22587                                0
## 383   24.62423  27.87132                                0
## 384   28.74743  26.30253                                0
## 385   24.21355  22.83641                                0
## 386   27.73169  27.00616                                0
## 387   24.93087  24.89802                                0
## 388   27.00068  27.07461                                0
## 389   30.91034  33.22382                                0
## 390   32.49008  24.34497                                0
## 391   28.91992  27.04723                                0
## 392   29.79329  29.48939                                0
## 393   30.90486  29.14442                                0
## 394   34.04517  28.02738                                0
## 395   24.56674  30.49692                                0
## 396   36.33128  26.63929                                0
## 397   29.91102  31.67693                                0
## 398   33.49213  27.80014                                0
## 399   25.11704  30.19576                                0
## 400   28.83504  26.25325                                0
## 401   27.91513  26.86379                                0
## 402   25.19370  26.42026                                0
## 403   29.15537  28.70089                                1
## 404   32.91444  26.31896                                0
## 405   36.10678  30.22040                                0
## 406   26.66667  33.11431                                0
## 407   25.90554  24.65435                                0
## 408   31.58111  27.16769                                0
## 409   28.22998  31.62218                                0
## 410   35.91513  27.05270                                0
## 411   25.67830  25.48939                                0
## 412   33.16632  27.35661                                0
## 413   33.76044  27.87680                                1
## 414   27.61944  29.23477                                0
## 415   33.42094  28.96920                                0
## 416   28.49008  28.27379                                0
## 417   32.61602  33.79329                                0
## 418   28.72279  33.90554                                0
## 419   26.97331  28.70363                                1
## 420   29.06776  25.50856                                0
## 421   33.47570  27.01164                                0
## 422   32.99932  23.98084                                0
## 423   34.22313  31.57837                                0
## 424   29.56879  28.61328                                0
## 425   27.70705  26.62012                                0
## 426   28.10404  33.88912                                0
## 427   30.26146  27.05818                                0
## 428   36.61875  28.66256                                0
## 429   23.48802  24.48186                                0
## 430   31.70431  28.47365                                3
## 431   33.71663  33.76044                                0
## 432   32.04381  33.44011                                0
## 433   33.37988  24.93361                                0
## 434   33.01300  29.18001                                0
## 435   34.93224  26.55168                                0
## 436   26.23956  32.72553                                0
## 437   29.31417  32.75017                                0
## 438   26.69131  32.48734                                0
## 439   30.91034  29.18001                                0
## 440   29.98768  24.34771                                0
## 441   28.61328  23.90965                                0
## 442   30.28884  25.13073                                0
## 443   28.91992  25.50582                                2
## 444   28.91992  29.26215                                0
## 445   30.46954  26.70500                                0
## 446   33.00753  27.24162                                0
## 447   30.78439  31.50992                                0
## 448   33.07050  33.17180                                0
## 449   33.62628  26.46680                                0
## 450   32.89802  26.55168                                0
## 451   30.81999  27.49350                                0
## 452   25.12252  30.45038                                0
## 453   28.91992  31.67967                                0
## 454   31.13210  26.80630                                0
## 455   33.94387  28.27105                                0
## 456   25.30322  30.00958                                0
## 457   29.24846  22.89391                                0
## 458   26.67214  27.32101                                0
## 459   32.28200  30.52156                                0
## 460   30.94867  25.26215                                0
## 461   26.94319  26.04791                                0
## 462   29.35797  30.54073                                0
## 463   28.40520  29.83162                                0
## 464   26.59822  26.53525                                0
## 465   26.47775  24.28747                                0
## 466   32.61054  26.62834                                0
## 467   27.74538  27.83025                                0
## 468   35.53183  28.06023                                0
## 469   29.29774  23.21971                                0
## 470   27.84120  30.44490                                0
## 471   27.46064  30.35181                                0
## 472   28.78850  28.10404                                0
## 473   32.28200  29.75770                                0
## 474   23.03080  28.44353                                0
## 475   29.94935  22.06434                                0
## 476   30.48597  29.40178                                0
## 477   32.14511  25.98220                                0
## 478   23.74264  29.21834                                0
## 479   27.37577  26.00137                                0
## 480   31.69610  29.83436                                0
## 481   29.24572  22.55168                                0
## 482   30.46407  24.52019                                0
## 483   30.10815  25.09240                                0
## 484   30.64203  26.46954                                0
## 485   31.79740  28.19439                                0
## 486   29.02396  28.95003                                0
## 487   33.06776  30.58727                                0
## 488   29.25667  30.38741                                0
## 489   30.32991  30.43121                                0
## 490   33.11431  27.39767                                0
## 491   27.27995  29.35524                                0
## 492   29.07050  23.41136                                0
## 493   28.93908  27.68241                                0
## 494   29.83162  26.84736                                0
## 495   28.68446  26.86105                                0
## 496   29.58522  29.20739                                1
## 497   26.74880  30.17385                                0
## 498   32.95003  31.14031                                0
## 499   34.39562  24.82957                                1
## 500   29.39630  27.07461                                0
## 501   27.99452  21.65092                                0
## 502   33.46475  29.18275                                0
## 503   31.15400  24.63518                                0
## 504   32.04654  26.11362                                0
## 505   32.54757  28.43806                                0
## 506   32.73648  27.34018                                0
## 507   29.01574  29.53867                                0
## 508   30.31075  26.55715                                0
## 509   35.96715  25.56879                                0
## 510   29.97399  29.87269                                0
## 511   30.01232  29.70294                                0
## 512   29.45380  30.63655                                0
## 513   24.77755  30.08350                                0
## 514   28.27652  34.06160                                0
## 515   29.66735  29.77687                                0
## 516   27.03080  29.00753                                0
## 517   27.97810  27.01164                                0
## 518   27.68241  29.33881                                0
## 519   28.05749  24.84873                                0
## 520   26.94319  30.04517                                0
## 521   30.73238  32.36961                                0
## 522   26.81999  27.78645                                0
## 523   23.43053  24.32580                                0
## 524   27.43326  32.55031                                0
## 525   32.60780  27.91513                                0
## 526   29.47023  32.77755                                0
## 527   33.40999  29.97125                                0
## 528   28.62971  22.97057                                0
## 529   27.03080  30.52704                                0
## 530   23.83847  26.21218                                0
## 531   27.14579  35.53730                                0
## 532   28.23819  25.61259                                0
## 533   33.28679  26.36550                                0
## 534   27.93703  31.30732                                0
## 535   32.12868  30.46954                                0
## 536   30.99247  33.32512                                0
## 537   22.34086  26.65298                                0
## 538   30.17933  25.94114                                0
## 539   30.32170  28.09582                                0
## 540   31.28816  32.41068                                0
## 541   28.21355  27.19781                                0
## 542   27.94251  26.32444                                0
## 543   24.38604  29.54962                                0
## 544   29.35524  36.65708                                0
## 545   31.06913  28.45448                                0
## 546   30.09993  32.95277                                0
## 547   29.48665  27.21424                                0
## 548   28.44079  26.99795                                0
## 549   33.58522  30.51882                                0
## 550   30.06708  30.78987                                0
## 551   29.75770  28.76112                                0
## 552   30.92950  27.43326                                0
## 553   32.74196  27.66872                                0
## 554   29.75770  29.30322                                0
## 555   26.65298  28.02738                                0
## 556   32.43258  28.74196                                0
## 557   28.67077  29.22108                                0
## 558   23.83299  26.53525                                0
## 559   35.96715  26.63381                                0
## 560   25.65914  29.12252                                0
## 561   33.10609  28.89528                                0
## 562   29.01300  22.62834                                0
## 563   27.04175  27.61944                                0
## 564   35.64134  33.34428                                0
## 565   33.49213  27.49624                                0
## 566   29.75770  26.54346                                0
## 567   32.61602  31.66324                                0
## 568   26.06708  32.43258                                0
## 569   26.44216  28.19165                                0
## 570   30.13826  28.10130                                0
## 571   30.31075  32.99932                                0
## 572   30.42574  29.28679                                0
## 573   29.35797  24.79124                                0
## 574   33.01848  24.91718                                0
## 575   30.52156  25.51951                                0
## 576   26.03970  32.45175                                0
## 577   35.96715  30.19028                                0
## 578   25.32786  31.74538                                0
## 579   25.34976  29.08693                                0
## 580   21.76318  34.35455                                0
## 581   28.65161  29.90007                                0
## 582   32.35866  32.27926                                0
## 583   24.58590  31.58385                                0
## 584   28.17522  26.02327                                0
## 585   29.64819  27.97810                                0
## 586   30.08624  24.42710                                0
## 587   30.68036  28.44079                                0
## 588   28.12868  24.11499                                0
## 589   30.48323  26.22861                                0
## 590   30.38741  36.46543                                0
## 591   33.75222  26.29158                                0
## 592   32.75565  28.72279                                0
## 593   32.56947  23.88775                                0
## 594   30.07529  33.05681                                2
## 595   27.32375  28.63518                                0
## 596   34.02053  28.10130                                0
## 597   28.39973  25.44832                                0
## 598   30.39288  26.36003                                0
## 599   30.73785  28.33128                                0
## 600   29.06502  33.17180                                0
## 601   27.03080  27.73169                                0
## 602   29.75496  31.39220                                0
## 603   24.61602  24.23272                                0
## 604   32.73101  26.59548                                0
## 605   31.17317  28.87337                                0
## 606   27.45243  23.44969                                0
## 607   27.49076  23.87132                                0
## 608   27.34292  33.65092                                0
## 609   31.54825  31.46886                                0
## 610   33.48939  34.02053                                0
## 611   34.95140  26.20945                                0
## 612   32.35866  30.81999                                0
## 613   30.58453  31.17591                                0
## 614   28.26283  31.37303                                0
## 615   29.77413  24.07940                                0
## 616   29.59069  29.65914                                3
## 617   30.31348  22.80082                                0
## 618   32.00821  28.53662                                0
## 619   31.92608  23.17043                                0
## 620   30.59001  27.69610                                0
## 621   30.10267  29.71663                                0
## 622   32.83504  24.44353                                0
## 623   35.64134  29.24025                                0
## 624   30.94319  29.79329                                0
## 625   26.92129  28.54757                                0
## 626   24.36961  26.49692                                0
## 627   30.08624  23.06639                                0
## 628   25.31691  26.77618                                0
## 629   33.36345  22.16564                                0
## 630   32.51198  25.23751                                0
## 631   35.85216  29.45106                                2
## 632   28.73101  25.54962                                0
## 633   29.33881  23.02806                                0
## 634   29.33881  28.36687                                0
## 635   29.39630  24.44627                                0
## 636   33.25667  24.86516                                0
## 637   30.06434  27.59206                                0
## 638   30.03149  25.93292                                0
## 639   27.39493  26.05613                                0
## 640   30.19849  32.13963                                1
## 641   29.31691  32.42710                                0
## 642   35.83847  32.63518                                0
## 643   28.47365  26.99521                                0
## 644   32.09035  25.67830                                0
## 645   29.37166  32.68172                                0
## 646   23.96167  32.48186                                0
## 647   25.86721  32.88980                                0
## 648   33.00753  23.62218                                0
## 649   32.01643  24.73374                                0
## 650   26.27515  29.73580                                0
## 651   29.68104  27.95072                                0
## 652   27.68241  31.49624                                0
## 653   29.35797  36.61875                                0
## 654   29.40178  28.38604                                0
## 655   27.03080  30.60917                                0
## 656   29.40999  32.31759                                0
## 657   28.06023  30.61739                                0
## 658   25.63997  28.91170                                0
## 659   30.32991  33.01300                                0
## 660   27.24162  29.29227                                0
## 661   31.50992  24.15606                                0
## 662   29.88912  28.81040                                0
## 663   36.06845  30.45311                                1
## 664   32.87337  23.48802                                0
## 665   32.53114  35.62218                                0
## 666   31.14031  29.62081                                2
## 667   28.91992  28.96920                                0
## 668   26.26968  26.13005                                0
## 669   29.03217  33.02396                                0
## 670   29.64545  27.96441                                0
## 671   31.52361  30.27242                                0
## 672   35.24435  35.81930                                0
## 673   26.36277  26.15469                                0
## 674   32.47091  28.73922                                0
## 675   32.76112  35.85216                                0
## 676   30.11910  25.86448                                0
## 677   30.88569  33.56879                                0
## 678   28.25736  29.16359                                0
## 679   27.01711  25.77960                                0
## 680   28.42163  30.89117                                0
## 681   32.03285  22.91307                                0
## 682   30.52704  28.39699                                0
## 683   28.15332  25.57700                                1
## 684   31.21697  33.13347                                0
## 685   28.97741  27.40315                                0
## 686   28.85969  33.02943                                0
## 687   30.04517  29.77687                                0
## 688   29.55236  31.45243                                0
## 689   28.10951  29.31417                                0
## 690   29.31417  26.88296                                0
## 691   28.99110  29.68378                                0
## 692   33.29500  29.56331                                0
## 693   27.01711  26.20123                                0
## 694   31.78371  26.91855                                0
## 695   31.86037  26.71869                                0
## 696   32.10951  25.69747                                0
## 697   28.02190  34.02327                                0
## 698   30.32991  27.01711                                0
## 699   32.33949  29.58522                                0
## 700   33.00753  27.94251                                0
## 701   32.35866  32.64066                                0
## 702   28.45996  29.35797                                0
## 703   32.89528  22.34086                                0
## 704   31.38946  29.86995                                0
## 705   26.73238  27.76728                                0
## 706   26.88569  28.10678                                0
## 707   27.43600  30.32991                                0
## 708   30.06708  23.04723                                0
## 709   33.79329  28.72827                                0
## 710   30.49418  28.51472                                0
## 711   27.99452  24.93087                                0
## 712   33.25667  23.87132                                0
## 713   36.27379  27.05544                                0
## 714   24.78850  31.45791                                0
## 715   30.39288  24.70637                                0
## 716   26.99247  28.08214                                0
## 717   27.45243  32.85147                                0
## 718   29.33881  22.24504                                0
## 719   29.13073  30.23682                                0
## 720   30.60917  27.71526                                0
## 721   26.03970  26.79808                                0
## 722   28.87611  36.17796                                0
## 723   33.14442  26.65298                                0
## 724   30.37098  26.31348                                0
## 725   29.16085  24.59138                                0
## 726   35.89596  28.82957                                0
## 727   32.96099  29.12252                                0
## 728   32.87337  29.23751                                0
## 729   31.23614  31.55921                                0
## 730   28.91718  29.62628                                0
## 731   32.56674  25.31691                                0
## 732   29.41547  29.45927                                0
## 733   28.62971  28.67351                                0
## 734   32.30390  27.70979                                0
## 735   34.06160  30.42574                                0
## 736   35.87680  28.24093                                0
## 737   30.13826  32.92266                                0
## 738   30.52704  34.02053                                0
## 739   29.19918  28.83504                                0
## 740   27.35661  32.39425                                0
## 741   30.54073  32.82683                                0
## 742   28.55031  29.24298                                0
## 743   31.87406  30.10267                                0
## 744   33.48939  27.75633                                0
## 745   32.09035  29.02396                                0
## 746   27.08830  23.10472                                0
## 747   33.40999  23.64134                                0
## 748   27.68241  23.67967                                0
## 749   33.71663  29.31691                                0
## 750   31.86037  32.88433                                0
## 751   30.29158  26.26694                                0
## 752   29.20465  28.50924                                0
## 753   28.23819  30.38741                                0
## 754   30.29706  28.84873                                0
## 755   27.93703  21.59343                                2
## 756   33.04586  27.98084                                0
## 757   28.38056  29.03217                                0
## 758   27.66324  29.81246                                0
## 759   32.87611  27.73443                                0
## 760   29.33881  25.28405                                0
## 761   27.93977  22.98973                                0
## 762   30.23956  25.88638                                0
## 763   27.43326  32.47091                                0
## 764   27.05544  24.65435                                0
## 765   33.54689  28.40520                                0
## 766   31.66872  30.02327                                0
## 767   33.16085  29.77413                                0
## 768   33.19918  23.43053                                0
## 769   28.55031  28.95003                                1
## 770   26.69131  27.79466                                0
## 771   26.88296  26.38193                                0
## 772   29.03217  25.21834                                0
## 773   27.35661  31.17043                                0
## 774   29.44559  28.70089                                0
## 775   27.43326  24.82683                                0
## 776   27.35661  23.37303                                0
## 777   33.19918  23.86858                                0
## 778   26.78166  28.85147                                0
## 779   32.28200  28.47091                                0
## 780   32.98836  32.87064                                0
## 781   31.17864  30.37098                                0
## 782   24.29295  26.03696                                0
## 783   28.91718  23.96715                                0
## 784   26.83915  32.48734                                0
## 785   33.16085  32.79398                                0
## 786   27.41410  24.30664                                0
## 787   29.14716  28.17522                                0
## 788   27.70979  25.27858                                0
## 789   27.97810  27.03080                                0
## 790   29.18275  29.36893                                0
## 791   33.16085  26.47775                                0
## 792   29.10883  26.32717                                0
## 793   29.41547  30.27515                                0
## 794   27.83573  29.90554                                0
## 795   29.14716  29.56605                                0
## 796   30.09993  26.09446                                0
## 797   28.93634  30.03970                                0
## 798   29.14716  31.69610                                0
## 799   29.39630  30.25599                                0
## 800   26.66667  32.31485                                0
## 801   27.01164  25.73580                                0
## 802   33.00753  24.13415                                0
## 803   28.76386  25.62628                                0
## 804   28.85969  29.96304                                0
## 805   28.93634  29.25667                                0
## 806   27.43326  27.40862                                0
## 807   28.72553  30.90486                                0
## 808   26.78166  28.08761                                0
## 809   28.62971  29.79329                                0
## 810   32.54757  28.58864                                0
## 811   28.72553  32.05476                                0
## 812   29.14716  31.42779                                0
## 813   27.27995  27.39767                                0
##     N_months_since_last_match_loser surface tourney_date      month winner_rank
## 1                                 0       3   2013-06-24 2013-06-01         116
## 2                                 0       3   2013-06-24 2013-06-01         135
## 3                                 0       3   2016-06-27 2016-06-01          41
## 4                                 0       2   2014-05-26 2014-05-01          37
## 5                                 0       1   2015-03-12 2015-03-01         104
## 6                                 0       2   2015-05-24 2015-05-01          91
## 7                                 0       1   2014-01-13 2014-01-01           8
## 8                                 0       1   2015-08-31 2015-08-01          41
## 9                                 0       2   2016-07-18 2016-07-01         421
## 10                                0       3   2014-06-09 2014-06-01          42
## 11                                0       2   2014-04-13 2014-04-01           6
## 12                                0       3   2017-07-03 2017-07-01          39
## 13                                0       3   2015-06-29 2015-06-01          82
## 14                                0       1   2013-10-28 2013-10-01           3
## 15                                0       3   2014-06-23 2014-06-01         132
## 16                                0       1   2015-02-09 2015-02-01          19
## 17                                0       1   2015-03-25 2015-03-01          34
## 18                                0       2   2014-07-07 2014-07-01          41
## 19                                0       1   2014-08-04 2014-08-01          15
## 20                                0       1   2015-02-23 2015-02-01         169
## 21                                0       2   2014-05-26 2014-05-01          59
## 22                                0       3   2014-06-09 2014-06-01          60
## 23                                0       1   2014-10-13 2014-10-01         116
## 24                                0       1   2015-07-27 2015-07-01         114
## 25                                0       3   2015-07-13 2015-07-01         161
## 26                                0       2   2015-05-24 2015-05-01          43
## 27                                0       1   2013-08-26 2013-08-01         128
## 28                                0       1   2014-01-13 2014-01-01           8
## 29                                0       3   2014-06-09 2014-06-01          69
## 30                                0       1   2015-10-05 2015-10-01          24
## 31                                0       1   2015-10-26 2015-10-01          49
## 32                                0       1   2015-08-16 2015-08-01        1034
## 33                                0       1   2014-08-04 2014-08-01          62
## 34                                0       2   2015-05-03 2015-05-01          62
## 35                                0       1   2015-03-12 2015-03-01          12
## 36                                0       2   2014-05-11 2014-05-01          19
## 37                                0       1   2015-02-16 2015-02-01          53
## 38                                0       1   2015-08-31 2015-08-01          56
## 39                                0       2   2014-05-11 2014-05-01          56
## 40                                0       1   2014-01-13 2014-01-01          79
## 41                                0       1   2014-03-06 2014-03-01          18
## 42                                0       1   2014-07-21 2014-07-01         142
## 43                                0       1   2015-10-05 2015-10-01          32
## 44                                0       2   2014-04-28 2014-04-01          62
## 45                                0       1   2014-10-05 2014-10-01           5
## 46                                0       2   2015-04-12 2015-04-01          18
## 47                                0       3   2015-06-15 2015-06-01          79
## 48                                0       2   2014-04-21 2014-04-01          65
## 49                                0       2   2014-04-07 2014-04-01         101
## 50                                0       2   2014-05-11 2014-05-01          67
## 51                                0       3   2014-06-09 2014-06-01          52
## 52                                0       1   2015-10-26 2015-10-01          48
## 53                                0       1   2015-08-31 2015-08-01          64
## 54                                0       1   2015-09-28 2015-09-01          74
## 55                                0       2   2015-07-20 2015-07-01          62
## 56                                0       1   2014-02-24 2014-02-01           8
## 57                                0       1   2014-08-25 2014-08-01          31
## 58                                0       1   2014-10-05 2014-10-01          31
## 59                                0       1   2014-02-10 2014-02-01          98
## 60                                0       1   2014-01-06 2014-01-01          85
## 61                                0       1   2015-02-16 2015-02-01          78
## 62                                0       2   2014-05-04 2014-05-01          68
## 63                                0       1   2015-08-16 2015-08-01          66
## 64                                0       1   2014-08-10 2014-08-01          65
## 65                                0       1   2014-03-06 2014-03-01          65
## 66                                0       3   2016-06-27 2016-06-01           2
## 67                                0       1   2015-08-10 2015-08-01         107
## 68                                0       1   2014-01-13 2014-01-01          25
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## 157                               0       3   2013-06-24 2013-06-01          37
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## 387                               0       3   2014-06-16 2014-06-01          57
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## 399                               0       1   2015-08-03 2015-08-01          86
## 400                               0       1   2014-02-03 2014-02-01          78
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## 402                               0       1   2015-08-31 2015-08-01          78
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## 407                               0       1   2014-08-25 2014-08-01          16
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## 409                               0       3   2015-06-29 2015-06-01          78
## 410                               0       1   2014-03-06 2014-03-01          12
## 411                               0       2   2014-05-04 2014-05-01          20
## 412                               0       1   2014-09-22 2014-09-01          57
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## 414                               0       2   2014-04-21 2014-04-01          53
## 415                               0       1   2014-07-28 2014-07-01          45
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## 417                               0       1   2014-03-06 2014-03-01          87
## 418                               0       2   2014-04-13 2014-04-01          47
## 419                               0       2   2014-05-04 2014-05-01           8
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## 426                               0       3   2015-06-29 2015-06-01           1
## 427                               0       1   2015-09-21 2015-09-01          52
## 428                               0       1   2015-10-11 2015-10-01          21
## 429                               0       3   2014-06-23 2014-06-01           9
## 430                               0       1   2014-01-13 2014-01-01          18
## 431                               0       2   2015-04-27 2015-04-01           2
## 432                               0       2   2015-05-24 2015-05-01          55
## 433                               0       2   2014-04-13 2014-04-01          57
## 434                               0       2   2014-07-27 2014-07-01          52
## 435                               0       1   2014-02-03 2014-02-01          79
## 436                               0       2   2014-04-13 2014-04-01         101
## 437                               0       2   2014-04-21 2014-04-01          28
## 438                               0       3   2014-06-16 2014-06-01          77
## 439                               0       1   2014-10-13 2014-10-01          36
## 440                               0       2   2015-04-12 2015-04-01          14
## 441                               0       2   2015-04-12 2015-04-01          18
## 442                               0       1   2015-08-10 2015-08-01          12
## 443                               0       1   2015-01-11 2015-01-01          92
## 444                               0       1   2015-01-11 2015-01-01          92
## 445                               0       1   2014-08-10 2014-08-01          52
## 446                               0       1   2014-08-10 2014-08-01           3
## 447                               0       1   2015-09-21 2015-09-01         107
## 448                               0       1   2014-08-17 2014-08-01          54
## 449                               0       1   2015-03-12 2015-03-01          70
## 450                               0       3   2014-06-16 2014-06-01          63
## 451                               0       1   2014-08-10 2014-08-01          24
## 452                              11       1   2014-08-25 2014-08-01          65
## 453                               0       1   2015-01-11 2015-01-01          92
## 454                               0       1   2015-03-12 2015-03-01          88
## 455                               0       1   2015-08-31 2015-08-01          19
## 456                               0       1   2015-10-11 2015-10-01          43
## 457                               0       1   2015-08-16 2015-08-01          15
## 458                               0       3   2014-06-09 2014-06-01          78
## 459                               0       1   2014-10-05 2014-10-01          35
## 460                               0       1   2014-10-27 2014-10-01          33
## 461                               0       1   2015-08-10 2015-08-01          87
## 462                               0       1   2015-10-11 2015-10-01           7
## 463                               0       1   2015-02-02 2015-02-01          61
## 464                               0       3   2014-06-09 2014-06-01          89
## 465                               0       1   2014-10-05 2014-10-01          18
## 466                               0       1   2014-03-06 2014-03-01          40
## 467                               0       1   2014-03-19 2014-03-01           9
## 468                               0       3   2014-06-09 2014-06-01          42
## 469                               0       1   2014-08-04 2014-08-01          15
## 470                               0       1   2015-11-02 2015-11-01          40
## 471                               4       1   2015-02-02 2015-02-01         100
## 472                               0       3   2015-06-21 2015-06-01          92
## 473                               0       1   2014-10-05 2014-10-01          35
## 474                               0       1   2015-11-02 2015-11-01          18
## 475                               0       2   2015-08-03 2015-08-01         137
## 476                               0       1   2015-10-11 2015-10-01          15
## 477                               0       3   2014-06-23 2014-06-01          22
## 478                               0       1   2014-08-10 2014-08-01          65
## 479                               0       1   2014-09-29 2014-09-01          11
## 480                               0       1   2015-11-02 2015-11-01          28
## 481                               0       2   2015-05-10 2015-05-01          34
## 482                               0       3   2015-06-15 2015-06-01          13
## 483                               0       1   2015-07-27 2015-07-01          47
## 484                               0       2   2014-07-07 2014-07-01          29
## 485                               0       2   2015-08-03 2015-08-01          39
## 486                               0       2   2014-05-04 2014-05-01          10
## 487                               0       3   2014-06-15 2014-06-01          52
## 488                               0       3   2014-07-07 2014-07-01          98
## 489                               0       2   2014-07-27 2014-07-01          81
## 490                               3       1   2014-07-28 2014-07-01          56
## 491                               0       1   2014-08-25 2014-08-01           9
## 492                               0       1   2014-10-13 2014-10-01           7
## 493                               0       1   2015-01-19 2015-01-01          54
## 494                               7       1   2015-02-02 2015-02-01          89
## 495                               0       1   2015-02-23 2015-02-01          27
## 496                               0       1   2015-03-25 2015-03-01          74
## 497                               0       3   2015-06-29 2015-06-01           9
## 498                               1       2   2015-04-12 2015-04-01          20
## 499                               0       2   2015-04-20 2015-04-01         124
## 500                               0       1   2015-10-26 2015-10-01           7
## 501                               0       3   2014-06-16 2014-06-01          14
## 502                               0       1   2015-03-12 2015-03-01          12
## 503                               0       2   2015-05-24 2015-05-01          35
## 504                               0       1   2014-01-06 2014-01-01          35
## 505                               0       1   2014-02-24 2014-02-01           8
## 506                               0       3   2014-06-16 2014-06-01          25
## 507                               0       3   2014-06-23 2014-06-01         119
## 508                               0       2   2014-07-21 2014-07-01         105
## 509                               0       1   2015-02-16 2015-02-01          29
## 510                               0       3   2015-06-08 2015-06-01          63
## 511                               0       3   2015-06-21 2015-06-01          59
## 512                               0       1   2015-11-15 2015-11-01           5
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## 514                               0       1   2015-08-31 2015-08-01           1
## 515                               0       1   2015-10-11 2015-10-01          24
## 516                               0       2   2014-05-26 2014-05-01          65
## 517                               0       2   2014-05-26 2014-05-01           1
## 518                               0       1   2015-01-19 2015-01-01           6
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## 520                               0       1   2015-08-10 2015-08-01          87
## 521                               0       1   2015-09-21 2015-09-01          10
## 522                               0       1   2014-03-19 2014-03-01           2
## 523                               0       1   2014-10-20 2014-10-01          11
## 524                               0       1   2014-10-20 2014-10-01          10
## 525                               0       1   2015-02-02 2015-02-01          56
## 526                               3       2   2015-02-09 2015-02-01          82
## 527                               0       1   2015-09-28 2015-09-01          30
## 528                               0       2   2014-05-04 2014-05-01           6
## 529                               0       2   2014-05-26 2014-05-01           8
## 530                               0       1   2014-09-15 2014-09-01          40
## 531                               6       1   2015-01-19 2015-01-01          32
## 532                               0       1   2015-08-10 2015-08-01           3
## 533                               0       1   2014-09-29 2014-09-01          62
## 534                               0       2   2014-05-26 2014-05-01          13
## 535                               0       1   2014-08-10 2014-08-01          25
## 536                               0       1   2014-10-13 2014-10-01          23
## 537                               0       1   2015-02-23 2015-02-01          42
## 538                               0       1   2015-03-12 2015-03-01          96
## 539                               0       1   2014-02-10 2014-02-01          27
## 540                               1       2   2014-05-18 2014-05-01          48
## 541                               0       1   2014-08-04 2014-08-01          21
## 542                               0       1   2014-08-10 2014-08-01          23
## 543                               0       2   2015-04-27 2015-04-01          21
## 544                               0       1   2015-10-26 2015-10-01          11
## 545                               0       1   2014-01-06 2014-01-01          32
## 546                               0       2   2014-05-04 2014-05-01          56
## 547                               0       3   2014-06-23 2014-06-01          44
## 548                               0       2   2014-07-21 2014-07-01         847
## 549                               0       1   2015-11-02 2015-11-01           8
## 550                               0       1   2015-10-11 2015-10-01           5
## 551                               0       1   2014-10-05 2014-10-01          92
## 552                               0       1   2014-10-20 2014-10-01          35
## 553                               0       1   2015-03-25 2015-03-01          64
## 554                               0       2   2015-04-27 2015-04-01          41
## 555                               0       2   2015-05-24 2015-05-01          10
## 556                               0       1   2014-01-13 2014-01-01           6
## 557                               0       1   2014-10-13 2014-10-01         127
## 558                               0       1   2014-10-27 2014-10-01          10
## 559                               0       1   2015-02-16 2015-02-01          29
## 560                               0       1   2015-03-12 2015-03-01          42
## 561                               0       2   2015-05-10 2015-05-01           8
## 562                               0       3   2015-06-08 2015-06-01          10
## 563                               0       2   2014-04-21 2014-04-01          50
## 564                               0       1   2014-10-20 2014-10-01          31
## 565                               0       1   2015-01-19 2015-01-01          72
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## 567                               0       1   2014-01-13 2014-01-01          61
## 568                               0       2   2014-02-10 2014-02-01          92
## 569                               0       1   2014-03-19 2014-03-01          62
## 570                               0       2   2014-05-18 2014-05-01          54
## 571                               0       2   2014-07-21 2014-07-01         105
## 572                               0       1   2015-08-31 2015-08-01           5
## 573                               0       1   2015-10-11 2015-10-01           7
## 574                               0       3   2014-06-23 2014-06-01          65
## 575                               0       1   2014-10-05 2014-10-01          82
## 576                               0       1   2014-10-13 2014-10-01           8
## 577                               0       1   2015-02-16 2015-02-01          29
## 578                               1       1   2015-10-19 2015-10-01          72
## 579                               0       1   2014-02-03 2014-02-01          37
## 580                               0       1   2014-02-10 2014-02-01         119
## 581                               4       1   2014-02-10 2014-02-01         134
## 582                               0       1   2014-08-10 2014-08-01           6
## 583                               0       3   2015-06-15 2015-06-01          51
## 584                               0       2   2015-07-27 2015-07-01          32
## 585                               1       1   2015-08-31 2015-08-01          60
## 586                               0       1   2015-10-19 2015-10-01           5
## 587                               0       2   2014-07-21 2014-07-01          38
## 588                               0       1   2014-08-04 2014-08-01          13
## 589                               0       3   2015-06-21 2015-06-01          13
## 590                               0       1   2015-08-16 2015-08-01           5
## 591                               0       1   2014-02-17 2014-02-01         126
## 592                               0       1   2014-09-22 2014-09-01          28
## 593                               0       1   2014-10-27 2014-10-01           6
## 594                               2       1   2015-01-05 2015-01-01          98
## 595                               0       2   2015-04-27 2015-04-01          74
## 596                               0       1   2015-09-28 2015-09-01          17
## 597                               0       1   2014-02-10 2014-02-01           7
## 598                               0       2   2014-04-07 2014-04-01          29
## 599                               0       1   2014-08-10 2014-08-01          34
## 600                               0       2   2015-02-16 2015-02-01          50
## 601                               0       2   2014-05-26 2014-05-01           8
## 602                               0       1   2014-09-29 2014-09-01          37
## 603                               0       2   2015-05-17 2015-05-01          74
## 604                               0       1   2014-02-24 2014-02-01          63
## 605                               0       2   2014-04-07 2014-04-01          61
## 606                               0       1   2014-10-27 2014-10-01           8
## 607                               0       1   2014-11-09 2014-11-01           6
## 608                               0       1   2015-02-09 2015-02-01          41
## 609                               1       2   2015-05-03 2015-05-01          24
## 610                               0       1   2015-09-28 2015-09-01           8
## 611                               0       1   2014-02-10 2014-02-01          80
## 612                               0       1   2014-08-10 2014-08-01           6
## 613                               0       1   2014-09-22 2014-09-01          48
## 614                               0       1   2014-09-22 2014-09-01          21
## 615                               0       1   2015-01-05 2015-01-01           4
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## 617                               0       1   2015-08-10 2015-08-01          24
## 618                               0       1   2015-10-19 2015-10-01          34
## 619                               1       1   2015-10-19 2015-10-01          44
## 620                               0       2   2014-05-18 2014-05-01          29
## 621                               0       1   2015-02-09 2015-02-01          86
## 622                               0       3   2014-06-09 2014-06-01           4
## 623                               0       1   2014-10-20 2014-10-01          31
## 624                               0       1   2015-03-12 2015-03-01          48
## 625                               0       1   2015-08-31 2015-08-01           9
## 626                               0       1   2015-09-28 2015-09-01          19
## 627                               0       1   2015-10-19 2015-10-01           5
## 628                               0       1   2014-03-06 2014-03-01          31
## 629                               0       3   2014-07-07 2014-07-01          43
## 630                               0       1   2014-10-05 2014-10-01           5
## 631                               2       1   2015-01-05 2015-01-01          27
## 632                               0       1   2015-02-09 2015-02-01          15
## 633                               0       1   2015-10-05 2015-10-01           8
## 634                               0       1   2015-10-05 2015-10-01           8
## 635                               0       1   2015-10-26 2015-10-01           7
## 636                               0       1   2014-11-09 2014-11-01           2
## 637                               0       2   2015-05-10 2015-05-01          14
## 638                               0       3   2015-06-29 2015-06-01          54
## 639                               0       2   2015-04-20 2015-04-01          31
## 640                               0       3   2015-06-29 2015-06-01          12
## 641                               0       1   2015-10-11 2015-10-01          11
## 642                               0       1   2014-02-03 2014-02-01          12
## 643                               0       2   2014-02-10 2014-02-01          18
## 644                               0       2   2014-05-04 2014-05-01           5
## 645                               0       2   2014-05-11 2014-05-01          30
## 646                               0       3   2014-06-09 2014-06-01          35
## 647                               0       1   2014-08-10 2014-08-01          19
## 648                               0       1   2014-08-10 2014-08-01           3
## 649                               6       2   2015-02-09 2015-02-01          75
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## 651                               0       2   2015-04-27 2015-04-01         174
## 652                               0       2   2015-08-03 2015-08-01          67
## 653                               0       1   2015-10-11 2015-10-01           7
## 654                               0       1   2015-10-11 2015-10-01          10
## 655                               0       2   2014-05-26 2014-05-01           8
## 656                               0       1   2014-08-25 2014-08-01           4
## 657                               0       1   2014-09-29 2014-09-01          60
## 658                               0       2   2014-04-21 2014-04-01          23
## 659                               0       2   2014-07-27 2014-07-01          81
## 660                               0       1   2014-08-10 2014-08-01           9
## 661                               0       2   2015-04-20 2015-04-01          25
## 662                               0       2   2014-02-17 2014-02-01          42
## 663                               0       2   2014-04-28 2014-04-01          16
## 664                               0       3   2014-06-23 2014-06-01           4
## 665                               0       1   2014-10-13 2014-10-01           5
## 666                               2       1   2015-01-05 2015-01-01          33
## 667                               0       1   2015-01-11 2015-01-01          92
## 668                               0       1   2014-01-13 2014-01-01          51
## 669                               1       1   2014-09-29 2014-09-01           6
## 670                               0       2   2015-05-10 2015-05-01           5
## 671                               0       1   2015-08-31 2015-08-01          25
## 672                               0       1   2014-02-24 2014-02-01          48
## 673                               0       1   2014-08-25 2014-08-01          19
## 674                               0       1   2014-10-20 2014-10-01          21
## 675                               0       1   2015-01-05 2015-01-01          10
## 676                               0       1   2015-02-09 2015-02-01          19
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## 678                               0       1   2015-08-16 2015-08-01           2
## 679                               0       1   2015-10-05 2015-10-01          14
## 680                               0       1   2015-02-02 2015-02-01          20
## 681                               0       2   2014-04-13 2014-04-01           6
## 682                               0       2   2014-05-26 2014-05-01          25
## 683                               0       1   2014-10-27 2014-10-01          21
## 684                               0       2   2015-02-02 2015-02-01          32
## 685                               0       1   2015-02-02 2015-02-01          46
## 686                               0       2   2015-04-12 2015-04-01           5
## 687                               0       2   2015-05-03 2015-05-01          14
## 688                               0       1   2015-08-31 2015-08-01          22
## 689                               0       1   2014-07-28 2014-07-01          14
## 690                               0       2   2015-05-17 2015-05-01          41
## 691                               0       3   2015-06-15 2015-06-01          19
## 692                               0       1   2015-08-16 2015-08-01          26
## 693                               1       1   2015-10-05 2015-10-01          14
## 694                               0       1   2014-01-13 2014-01-01           3
## 695                               0       2   2014-02-10 2014-02-01           5
## 696                               0       2   2014-05-11 2014-05-01           5
## 697                               0       2   2014-05-26 2014-05-01          20
## 698                               0       2   2014-07-27 2014-07-01          81
## 699                               0       1   2014-08-04 2014-08-01           7
## 700                               0       1   2014-08-10 2014-08-01           3
## 701                               0       1   2014-08-10 2014-08-01           6
## 702                               0       1   2015-02-16 2015-02-01          21
## 703                               0       1   2015-02-23 2015-02-01           9
## 704                               0       2   2015-04-06 2015-04-01          30
## 705                               2       2   2015-05-24 2015-05-01          29
## 706                               0       2   2015-07-20 2015-07-01          81
## 707                               0       1   2015-09-21 2015-09-01          23
## 708                               0       1   2015-10-11 2015-10-01           5
## 709                               0       2   2015-05-24 2015-05-01           2
## 710                               9       2   2014-04-13 2014-04-01          25
## 711                               0       3   2014-06-16 2014-06-01          14
## 712                               0       1   2014-11-09 2014-11-01           2
## 713                               0       3   2015-06-08 2015-06-01          27
## 714                               3       2   2015-07-20 2015-07-01          68
## 715                               0       2   2014-04-07 2014-04-01          29
## 716                               0       2   2014-05-11 2014-05-01           8
## 717                               0       1   2014-10-27 2014-10-01           8
## 718                               0       1   2015-01-19 2015-01-01           7
## 719                               0       1   2015-10-19 2015-10-01          21
## 720                               0       2   2014-05-26 2014-05-01          24
## 721                               0       1   2014-10-13 2014-10-01           8
## 722                               0       2   2015-05-03 2015-05-01          23
## 723                               0       2   2015-05-24 2015-05-01           8
## 724                               0       1   2015-08-31 2015-08-01          18
## 725                               0       1   2014-02-24 2014-02-01          23
## 726                               0       2   2014-02-24 2014-02-01          12
## 727                               0       2   2014-05-18 2014-05-01         100
## 728                               0       3   2014-06-23 2014-06-01           4
## 729                               0       2   2015-02-09 2015-02-01          31
## 730                               0       2   2015-05-03 2015-05-01           4
## 731                               0       1   2014-03-06 2014-03-01           8
## 732                               0       1   2015-11-02 2015-11-01           6
## 733                               0       1   2015-01-19 2015-01-01           3
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## 735                               0       1   2015-08-31 2015-08-01           2
## 736                               1       1   2014-02-17 2014-02-01          12
## 737                               0       2   2014-05-18 2014-05-01          54
## 738                               1       2   2014-05-26 2014-05-01          25
## 739                               0       3   2014-06-09 2014-06-01           3
## 740                               0       1   2014-09-22 2014-09-01          11
## 741                               0       1   2014-10-13 2014-10-01          70
## 742                               0       1   2015-01-05 2015-01-01          26
## 743                               0       1   2015-08-31 2015-08-01          29
## 744                               0       1   2015-09-28 2015-09-01           8
## 745                               0       2   2014-05-04 2014-05-01           5
## 746                               0       3   2014-06-23 2014-06-01           2
## 747                               0       1   2015-01-04 2015-01-01           2
## 748                               0       1   2015-01-19 2015-01-01           6
## 749                               0       2   2015-04-27 2015-04-01           2
## 750                               0       2   2014-05-04 2014-05-01          16
## 751                               0       2   2014-07-14 2014-07-01          86
## 752                               0       1   2015-08-16 2015-08-01           8
## 753                               0       1   2015-08-16 2015-08-01           1
## 754                               0       1   2014-03-06 2014-03-01          33
## 755                               0       2   2014-05-26 2014-05-01          13
## 756                               0       1   2014-08-25 2014-08-01           3
## 757                               0       1   2014-10-20 2014-10-01           3
## 758                               0       1   2015-01-19 2015-01-01           1
## 759                               0       2   2015-02-16 2015-02-01           9
## 760                               0       1   2015-10-05 2015-10-01           8
## 761                               0       2   2014-05-11 2014-05-01           1
## 762                               0       2   2014-05-18 2014-05-01          33
## 763                               0       1   2014-10-20 2014-10-01          10
## 764                               0       1   2015-10-19 2015-10-01          14
## 765                               0       1   2015-10-19 2015-10-01           8
## 766                               0       1   2014-02-24 2014-02-01          15
## 767                               0       1   2014-10-05 2014-10-01           3
## 768                               0       1   2014-10-20 2014-10-01           2
## 769                               2       1   2015-01-05 2015-01-01          26
## 770                               0       3   2015-06-08 2015-06-01           9
## 771                               0       1   2015-08-16 2015-08-01           9
## 772                               0       1   2014-09-29 2014-09-01           6
## 773                               6       2   2015-04-06 2015-04-01          32
## 774                               0       1   2014-10-05 2014-10-01          14
## 775                               0       1   2014-10-27 2014-10-01           1
## 776                               0       1   2014-09-29 2014-09-01           1
## 777                               0       1   2014-10-20 2014-10-01           2
## 778                               0       1   2014-03-06 2014-03-01           2
## 779                               0       2   2014-07-14 2014-07-01           7
## 780                               0       1   2014-08-04 2014-08-01           3
## 781                               0       1   2015-01-19 2015-01-01          33
## 782                               0       2   2015-04-12 2015-04-01           6
## 783                               0       2   2015-05-03 2015-05-01           4
## 784                               0       1   2014-03-19 2014-03-01           6
## 785                               0       1   2014-10-05 2014-10-01           3
## 786                               0       1   2014-10-13 2014-10-01          11
## 787                               0       2   2015-07-27 2015-07-01          10
## 788                               0       2   2014-02-17 2014-02-01           1
## 789                               0       2   2014-05-26 2014-05-01           1
## 790                               0       3   2014-06-23 2014-06-01          17
## 791                               0       1   2014-10-05 2014-10-01           3
## 792                               0       1   2014-10-27 2014-10-01           5
## 793                               0       1   2015-11-02 2015-11-01           6
## 794                               0       1   2015-03-25 2015-03-01           1
## 795                               0       2   2015-07-27 2015-07-01          10
## 796                               0       2   2015-05-03 2015-05-01           9
## 797                               0       2   2015-05-10 2015-05-01           7
## 798                               0       2   2015-07-27 2015-07-01          10
## 799                               0       1   2015-10-26 2015-10-01           7
## 800                               0       1   2014-01-13 2014-01-01           4
## 801                               0       2   2014-05-26 2014-05-01           2
## 802                               0       1   2014-08-10 2014-08-01           3
## 803                               0       1   2015-03-12 2015-03-01           3
## 804                               0       2   2015-04-12 2015-04-01           5
## 805                               0       1   2014-08-25 2014-08-01           7
## 806                               0       1   2014-10-20 2014-10-01          10
## 807                               0       2   2015-02-23 2015-02-01           4
## 808                               0       1   2014-02-24 2014-02-01           7
## 809                               0       1   2015-01-19 2015-01-01           3
## 810                               0       1   2014-02-24 2014-02-01           8
## 811                               0       2   2015-02-23 2015-02-01           4
## 812                               0       2   2015-07-27 2015-07-01          10
## 813                               0       1   2014-08-25 2014-08-01           9
##     loser_rank pp_p1_set_win_prob pp_p1_match_win_prob pp_p1_y
## 1            3          0.1976539           0.06008175    25.0
## 2            5          0.2377964           0.09706819    26.0
## 3            1          0.2335658           0.08922521    26.0
## 4           12          0.3336490           0.21716044    29.0
## 5            7          0.2861232           0.19965404    16.0
## 6           58          0.2675205           0.12994293    27.0
## 7            2          0.2556554           0.11073800    26.0
## 8            4          0.3417751           0.22430227    29.0
## 9            9          0.3804518           0.32512103    18.0
## 10           5          0.2763855           0.18925485    16.0
## 11           1          0.3020560           0.21956115    17.0
## 12          27          0.5038186           0.50709955    33.0
## 13          47          0.3234116           0.20370281    28.0
## 14           1          0.3851974           0.33131544    18.0
## 15          28          0.2893995           0.15601328    27.0
## 16           4          0.2903219           0.20444701    17.0
## 17           3          0.3047513           0.22262228    17.0
## 18           7          0.2460008           0.15303601    16.0
## 19           1          0.2798661           0.19164740    16.0
## 20          10          0.3491021           0.28143785    17.0
## 21          10          0.3609690           0.25792776    29.0
## 22          26          0.2520137           0.16199534    16.0
## 23           9          0.3224929           0.24603915    17.0
## 24          74          0.2859190           0.19984721    16.0
## 25          18          0.2612310           0.17162920    16.0
## 26          20          0.3968564           0.31528884    30.0
## 27          18          0.4574003           0.42190386    31.0
## 28           1          0.3257201           0.20012058    28.0
## 29          27          0.3326774           0.26064592    17.0
## 30           9          0.3992596           0.35130243    18.0
## 31          12          0.3509498           0.28370997    17.0
## 32          20          0.6077614           0.65866831    21.0
## 33          14          0.3851360           0.33125820    18.0
## 34          15          0.3373875           0.26578457    17.0
## 35           5          0.3905376           0.33890319    18.0
## 36           3          0.4415966           0.41342263    19.0
## 37           6          0.2860623           0.19996118    16.0
## 38          17          0.3769241           0.28005547    30.0
## 39          15          0.4663836           0.45006883    19.0
## 40          82          0.3395839           0.22224944    29.0
## 41           3          0.4002306           0.35277612    18.0
## 42          17          0.3731916           0.31481398    18.0
## 43           6          0.3410317           0.27033522    17.0
## 44           6          0.3379316           0.26677303    17.0
## 45          11          0.3944339           0.34433490    18.0
## 46           2          0.3278391           0.25327043    17.0
## 47          10          0.3227756           0.24730222    17.0
## 48          20          0.3210923           0.24417483    17.0
## 49           9          0.3906662           0.34131640    18.0
## 50          26          0.3609241           0.29793053    17.0
## 51          14          0.3185494           0.24258078    17.0
## 52          31          0.3937304           0.34408693    18.0
## 53          38          0.4239804           0.36077879    31.0
## 54          19          0.3375968           0.26562592    17.0
## 55          14          0.4363153           0.40606433    19.0
## 56           2          0.4436233           0.41596073    19.0
## 57           5          0.3716587           0.27081564    29.0
## 58           9          0.3625021           0.29949610    17.0
## 59          40          0.3368569           0.26505439    17.0
## 60          46          0.3451017           0.27639790    17.0
## 61          19          0.3640207           0.30176771    18.0
## 62          27          0.3366694           0.26730759    17.0
## 63           6          0.3385982           0.26677387    17.0
## 64           8          0.4588823           0.43883734    19.0
## 65          10          0.3477904           0.27930553    17.0
## 66           7          0.6788282           0.80491099    37.0
## 67          11          0.4949025           0.49237127    19.0
## 68          43          0.4223731           0.35795130    31.0
## 69          15          0.3393845           0.26972892    17.0
## 70          36          0.4282271           0.36794077    31.0
## 71          21          0.4264022           0.36579371    31.0
## 72           6          0.3830050           0.32826925    18.0
## 73          34          0.3613853           0.29845268    18.0
## 74          21          0.4009015           0.35381008    18.0
## 75          13          0.3423925           0.27309293    17.0
## 76          27          0.4483976           0.40507121    31.0
## 77           5          0.3277659           0.25250606    17.0
## 78          46          0.3803416           0.28738961    30.0
## 79          10          0.4268546           0.39133713    19.0
## 80          20          0.3482988           0.28076355    17.0
## 81          76          0.3318800           0.25878048    17.0
## 82          41          0.3815898           0.32638668    18.0
## 83          11          0.3858214           0.33242366    18.0
## 84          49          0.3712887           0.31409945    18.0
## 85           9          0.3406775           0.27047559    17.0
## 86          16          0.3736802           0.31517658    18.0
## 87          13          0.4481988           0.42276027    19.0
## 88          16          0.3546586           0.28890829    18.0
## 89          10          0.4466060           0.42050939    19.0
## 90          52          0.4920946           0.48827013    19.0
## 91          15          0.4573583           0.43681306    19.0
## 92          26          0.3853735           0.33231851    18.0
## 93           1          0.4355334           0.40397916    19.0
## 94          19          0.3631401           0.30151908    17.0
## 95           1          0.3960406           0.34656543    18.0
## 96          19          0.4303571           0.39647720    18.0
## 97          27          0.4026564           0.35676923    18.0
## 98           9          0.4362921           0.40583234    19.0
## 99           6          0.3856525           0.33272310    18.0
## 100         79          0.3976143           0.35058864    18.0
## 101          5          0.4786278           0.46070427    32.0
## 102          4          0.3676041           0.30660620    18.0
## 103          7          0.3916675           0.34158840    18.0
## 104          7          0.3803566           0.32432997    18.0
## 105         18          0.4582264           0.43785381    19.0
## 106         24          0.4864552           0.47515663    32.0
## 107          2          0.4149863           0.37445972    18.0
## 108         20          0.3923289           0.34169787    18.0
## 109         17          0.3748732           0.31726664    18.0
## 110         44          0.3659510           0.30534542    18.0
## 111          8          0.4515613           0.42825284    19.0
## 112         25          0.4461876           0.42039129    19.0
## 113         71          0.4681291           0.45249813    19.0
## 114         40          0.3720972           0.31337529    18.0
## 115         19          0.4382822           0.40863367    19.0
## 116         36          0.4220412           0.35983593    31.0
## 117         21          0.3817700           0.32788622    18.0
## 118         12          0.4744315           0.46180013    19.0
## 119          1          0.4393061           0.40957787    19.0
## 120         26          0.4173882           0.37762860    18.0
## 121         22          0.4801759           0.47038688    19.0
## 122         10          0.4902905           0.48212960    32.0
## 123         10          0.3792228           0.32278446    18.0
## 124         19          0.5462727           0.56903155    20.0
## 125         66          0.4538078           0.43231645    19.0
## 126         22          0.3879057           0.33597752    18.0
## 127          5          0.4565092           0.43511467    19.0
## 128         58          0.4163975           0.37667000    18.0
## 129         19          0.4367573           0.40637724    19.0
## 130         10          0.3721084           0.31327520    18.0
## 131         32          0.6757816           0.79675331    37.0
## 132         11          0.3982624           0.35117950    18.0
## 133        108          0.4987978           0.49818256    19.0
## 134          7          0.3716272           0.31206294    18.0
## 135         14          0.3904054           0.33916487    18.0
## 136          4          0.4275999           0.39312056    19.0
## 137         86          0.4645258           0.44711211    19.0
## 138          9          0.4862361           0.47942009    19.0
## 139          3          0.3820206           0.32692975    18.0
## 140         32          0.5181826           0.52696260    20.0
## 141        294          0.4469260           0.40394441    31.0
## 142         11          0.4010203           0.35406784    18.0
## 143         49          0.3997360           0.35206792    18.0
## 144         39          0.6215471           0.67760865    21.0
## 145         11          0.3775429           0.32041996    18.0
## 146         25          0.5013824           0.50206499    20.0
## 147         25          0.4941871           0.49130657    20.0
## 148         80          0.4506262           0.42759977    19.0
## 149         79          0.4408865           0.41234781    19.0
## 150          4          0.4009517           0.35379531    18.0
## 151        119          0.4170500           0.37802905    18.0
## 152         11          0.4670733           0.45087098    19.0
## 153         59          0.4448297           0.39933894    31.0
## 154         26          0.3903435           0.33907753    18.0
## 155         36          0.3845014           0.33140425    18.0
## 156         25          0.4329689           0.40072252    18.0
## 157         30          0.6393132           0.74248553    36.0
## 158         16          0.3871451           0.33477578    18.0
## 159         19          0.4570836           0.43621795    19.0
## 160         32          0.4106255           0.33782453    30.0
## 161         35          0.4011820           0.35444330    18.0
## 162         67          0.3907835           0.34160599    18.0
## 163        112          0.4776434           0.46666882    19.0
## 164         90          0.4629257           0.44517935    19.0
## 165         19          0.4292720           0.39495512    18.0
## 166         28          0.4154162           0.34576942    30.0
## 167          4          0.4718815           0.44799657    32.0
## 168         30          0.3917037           0.34131715    18.0
## 169          1          0.4321109           0.39896830    19.0
## 170         78          0.4055608           0.36113168    18.0
## 171         28          0.3918418           0.34086207    18.0
## 172         22          0.5799711           0.64596565    35.0
## 173         33          0.4613476           0.44237790    19.0
## 174         54          0.4525373           0.41355419    32.0
## 175         67          0.4875673           0.48155839    19.0
## 176        119          0.5660710           0.61991286    34.0
## 177          6          0.4351021           0.40344372    19.0
## 178         53          0.4764479           0.46501510    19.0
## 179         59          0.6599867           0.77774265    36.0
## 180         31          0.5057325           0.50855006    20.0
## 181        119          0.5699025           0.60376340    21.0
## 182         10          0.4163290           0.37608647    18.0
## 183         29          0.4051102           0.36022216    18.0
## 184         22          0.4879126           0.48198939    19.0
## 185         17          0.4643701           0.43427942    32.0
## 186         18          0.4587289           0.43841023    19.0
## 187         20          0.4048990           0.36014684    18.0
## 188         11          0.4497712           0.42555144    19.0
## 189         44          0.4943645           0.49188587    19.0
## 190         44          0.4419929           0.41397874    19.0
## 191         47          0.4454566           0.39965325    31.0
## 192         75          0.5812497           0.64758920    34.0
## 193         48          0.5234768           0.53505712    20.0
## 194         10          0.4245425           0.38796556    19.0
## 195         22          0.4700861           0.45543326    19.0
## 196         42          0.4681331           0.45243079    19.0
## 197         47          0.4736639           0.45161420    32.0
## 198         74          0.5680334           0.59995616    20.0
## 199         57          0.4923032           0.48864162    19.0
## 200         44          0.4955108           0.49331061    19.0
## 201         99          0.4771095           0.46588717    19.0
## 202         31          0.4695815           0.45463720    19.0
## 203         14          0.4578855           0.43735784    19.0
## 204         68          0.5665551           0.59856174    20.0
## 205         64          0.4434743           0.39831438    31.0
## 206         24          0.5299180           0.55554557    33.0
## 207          7          0.5062039           0.50928581    20.0
## 208         39          0.5968804           0.64305487    21.0
## 209         19          0.5300753           0.54493602    20.0
## 210         16          0.4940407           0.49110287    19.0
## 211          5          0.5914567           0.63533524    21.0
## 212         48          0.4894087           0.48421842    19.0
## 213         38          0.5159101           0.52377444    20.0
## 214         21          0.5283568           0.54231099    20.0
## 215         57          0.4304616           0.39708252    18.0
## 216         92          0.5535363           0.57900510    20.0
## 217         72          0.5036329           0.50542858    20.0
## 218         31          0.4884631           0.47852260    32.0
## 219         20          0.4832811           0.47509709    19.0
## 220         16          0.4611453           0.42819655    32.0
## 221          4          0.5023428           0.50419121    33.0
## 222         41          0.4780292           0.46721988    19.0
## 223        154          0.5703263           0.60431726    20.0
## 224         48          0.4766552           0.46530000    19.0
## 225         35          0.5123864           0.52291593    33.0
## 226         19          0.4250463           0.38889182    18.0
## 227        119          0.4615213           0.44274491    19.0
## 228         30          0.4578835           0.43723151    19.0
## 229         56          0.4656540           0.44920647    19.0
## 230         19          0.4377748           0.38595691    31.0
## 231         13          0.4804819           0.47082906    19.0
## 232         13          0.5545653           0.58129799    20.0
## 233          5          0.5201758           0.53015444    20.0
## 234         36          0.4695306           0.45466292    19.0
## 235         63          0.4936339           0.49053660    19.0
## 236         42          0.4386181           0.40900679    19.0
## 237         89          0.4445696           0.41748689    19.0
## 238         20          0.4775893           0.46655024    19.0
## 239        113          0.5636328           0.59351429    20.0
## 240         13          0.4499636           0.42542343    19.0
## 241          2          0.4934586           0.49021144    20.0
## 242         80          0.4344318           0.40294675    19.0
## 243         55          0.5539994           0.58031225    20.0
## 244         21          0.5566713           0.58402606    20.0
## 245         91          0.5624185           0.59142975    21.0
## 246         24          0.4971108           0.49568384    19.0
## 247         11          0.4418693           0.41347986    19.0
## 248         20          0.4925462           0.48885088    19.0
## 249         44          0.4369695           0.40673888    19.0
## 250         38          0.4480504           0.42256616    19.0
## 251         14          0.5017049           0.50253385    20.0
## 252        197          0.4462943           0.42053658    19.0
## 253         15          0.4579033           0.43750373    19.0
## 254         23          0.4427250           0.41526096    19.0
## 255        141          0.4428013           0.41677106    19.0
## 256         30          0.4744982           0.46193516    19.0
## 257         46          0.4501350           0.42587881    19.0
## 258         11          0.4466973           0.42089302    19.0
## 259         10          0.4650936           0.44787102    19.0
## 260         62          0.6030357           0.65106290    21.0
## 261         21          0.4542443           0.43174494    19.0
## 262        174          0.4856103           0.47853011    19.0
## 263         18          0.4830621           0.47475772    19.0
## 264         15          0.4984014           0.49702141    32.0
## 265         76          0.6045204           0.65354583    21.0
## 266         76          0.5519765           0.57695527    20.0
## 267         69          0.4571116           0.43632592    19.0
## 268         94          0.4494318           0.42522589    19.0
## 269         35          0.4650191           0.44799999    19.0
## 270         44          0.4954048           0.49146725    32.0
## 271          6          0.4481451           0.42268493    19.0
## 272         18          0.4844414           0.47151178    32.0
## 273         12          0.4792633           0.46897663    19.0
## 274         57          0.5400533           0.55943234    20.0
## 275         37          0.4596706           0.44008927    19.0
## 276         49          0.5323709           0.54813560    20.0
## 277         56          0.5880574           0.63026370    21.0
## 278         52          0.5140092           0.52081847    20.0
## 279         36          0.4850951           0.47784211    19.0
## 280         44          0.5744994           0.61027395    20.0
## 281         25          0.5400806           0.55982016    20.0
## 282         50          0.4771751           0.46620058    19.0
## 283         42          0.5336629           0.55012064    20.0
## 284         22          0.4745760           0.46210178    19.0
## 285         15          0.4754744           0.46342847    19.0
## 286         19          0.4866993           0.48014592    19.0
## 287         93          0.6339219           0.69443838    21.0
## 288         21          0.4756232           0.46386738    19.0
## 289        122          0.5222345           0.53286118    20.0
## 290         74          0.5346081           0.55160691    20.0
## 291         18          0.4793520           0.46151904    32.0
## 292         35          0.5063648           0.50952067    20.0
## 293          5          0.5466705           0.56914082    20.0
## 294         49          0.4850252           0.47764411    19.0
## 295        107          0.5110309           0.51989438    33.0
## 296         36          0.4634449           0.44553543    19.0
## 297         40          0.4976000           0.49642715    20.0
## 298         51          0.4873313           0.48108956    19.0
## 299         51          0.4794436           0.46934770    19.0
## 300         22          0.5273114           0.54071345    20.0
## 301         36          0.4814027           0.47229884    19.0
## 302         30          0.6397590           0.70138982    22.0
## 303         24          0.5245369           0.53666260    20.0
## 304         70          0.5304363           0.54495714    20.0
## 305         73          0.5333759           0.54968530    20.0
## 306         41          0.5387826           0.55765464    20.0
## 307         29          0.5243057           0.53609526    20.0
## 308         28          0.6103107           0.69524084    35.0
## 309         38          0.5511409           0.57594578    20.0
## 310         36          0.6148223           0.66756288    21.0
## 311         98          0.4891033           0.48373869    19.0
## 312         34          0.5092422           0.51378091    20.0
## 313        101          0.5358238           0.55335952    20.0
## 314         59          0.5165179           0.52455278    20.0
## 315         18          0.5366175           0.55445403    20.0
## 316        117          0.5092967           0.51385716    20.0
## 317         52          0.4719624           0.45860001    19.0
## 318         70          0.5861756           0.62749082    21.0
## 319         62          0.5520685           0.57734459    20.0
## 320        132          0.6532990           0.76555551    36.0
## 321          5          0.5447333           0.58293646    33.5
## 322         78          0.4835760           0.47560342    19.0
## 323         11          0.4918033           0.48774161    19.0
## 324         13          0.5298590           0.54438075    20.0
## 325         37          0.5763982           0.61333138    21.0
## 326         43          0.4770241           0.46588296    19.0
## 327         73          0.5764444           0.61286032    20.0
## 328         52          0.5895447           0.63239971    21.0
## 329         22          0.5291651           0.54356444    20.0
## 330         75          0.5308418           0.54574939    20.0
## 331         64          0.5073246           0.51089788    19.0
## 332        101          0.5150967           0.52229914    20.0
## 333         75          0.5029188           0.50434794    20.0
## 334         12          0.5139358           0.52076560    20.0
## 335         18          0.5496611           0.57402458    20.0
## 336         62          0.4924487           0.48876745    19.0
## 337         20          0.5019851           0.50296907    20.0
## 338         13          0.6633648           0.73518587    22.0
## 339          8          0.5555460           0.60250019    34.0
## 340         81          0.5338433           0.55033449    20.0
## 341         91          0.5640761           0.59499650    20.0
## 342         27          0.6709914           0.74392496    22.0
## 343         36          0.4963274           0.49452344    19.0
## 344         11          0.5333948           0.56127957    33.0
## 345         22          0.5071942           0.51076046    20.0
## 346         37          0.5220219           0.53286395    20.0
## 347         18          0.5102319           0.51519112    20.0
## 348         47          0.5630668           0.59343065    21.0
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## 707         57          0.6901544           0.77029129    22.0
## 708         33          0.6987985           0.78151376    22.0
## 709         14          0.6654032           0.78564445    37.0
## 710        329          0.7148332           0.80021422    23.0
## 711         57          0.7255517           0.81145570    23.0
## 712          8          0.7056523           0.79052604    23.0
## 713        106          0.7452196           0.83471974    23.0
## 714        296          0.7959216           0.88804013    24.0
## 715         91          0.8402162           0.92737754    25.0
## 716         31          0.7579921           0.85096265    23.0
## 717         28          0.7645161           0.85914963    24.0
## 718         66          0.6991681           0.83421487    37.0
## 719         78          0.7413651           0.83309093    23.0
## 720         49          0.6950101           0.82637648    37.0
## 721         74          0.7146716           0.80126815    23.0
## 722         25          0.7184483           0.80466817    23.0
## 723         10          0.6845698           0.81384504    37.0
## 724         41          0.7024700           0.83843284    37.0
## 725         91          0.7066847           0.79116441    22.0
## 726        116          0.7131018           0.79774076    23.0
## 727        110          0.8107634           0.90302570    24.0
## 728          3          0.7088975           0.84447374    37.0
## 729        100          0.7169674           0.80294503    23.0
## 730          7          0.7912070           0.88643327    24.0
## 731         31          0.7873272           0.88283966    24.0
## 732         12          0.7226574           0.81141776    23.0
## 733         15          0.7422309           0.88700443    39.0
## 734        127          0.7644326           0.90321890    39.0
## 735          5          0.6864157           0.81756370    37.0
## 736        118          0.7210478           0.80764012    23.0
## 737         71          0.7931393           0.88542391    24.0
## 738        153          0.7395774           0.87946966    38.0
## 739         60          0.7138036           0.79767131    23.0
## 740         22          0.7486077           0.84138214    23.0
## 741         73          0.7208383           0.80784298    23.0
## 742         52          0.7365602           0.82694550    23.0
## 743         87          0.6861332           0.81630358    37.0
## 744         48          0.7260433           0.81523460    23.0
## 745         10          0.7646951           0.85862546    23.5
## 746         13          0.7753528           0.91754077    39.0
## 747         11          0.7468133           0.83942584    23.0
## 748         11          0.7149112           0.85468118    38.0
## 749         23          0.7521781           0.84470821    23.0
## 750         67          0.7328894           0.81979417    23.0
## 751         97          0.7755409           0.86953168    23.0
## 752         27          0.7897522           0.88536535    24.0
## 753          5          0.7424635           0.83474929    23.0
## 754        126          0.7678445           0.86166506    24.0
## 755         80          0.7239434           0.86130878    38.0
## 756         24          0.7141829           0.85397893    38.0
## 757         75          0.8629751           0.94784713    25.0
## 758          4          0.7438453           0.88886701    38.0
## 759         28          0.7750173           0.86999131    24.0
## 760         44          0.7949618           0.89031586    24.0
## 761         14          0.8682362           0.95107609    25.0
## 762         96          0.7356079           0.82298391    23.0
## 763         21          0.7460769           0.83858005    23.0
## 764         84          0.7472637           0.83916435    23.0
## 765         22          0.7781921           0.87355746    24.0
## 766         75          0.7524260           0.84469686    23.0
## 767         29          0.7459665           0.83867246    23.0
## 768         11          0.7505281           0.84359161    23.0
## 769         41          0.8025939           0.89742564    24.0
## 770        502          0.7608068           0.85278500    23.0
## 771         44          0.7628659           0.85679551    24.0
## 772         56          0.7632120           0.85700836    23.0
## 773        346          0.7791175           0.87117923    24.0
## 774         43          0.7652301           0.85941114    23.0
## 775          7          0.7773555           0.87268274    24.0
## 776         10          0.7959491           0.89135500    24.0
## 777         28          0.8229185           0.91606600    25.0
## 778         13          0.7979393           0.89352022    24.0
## 779         78          0.8027920           0.89760293    24.0
## 780         25          0.8044174           0.89961375    24.0
## 781         92          0.7556995           0.89976230    39.0
## 782         56          0.7886817           0.88216292    24.0
## 783         11          0.8569729           0.94334404    25.0
## 784         34          0.7821027           0.87759970    24.0
## 785         30          0.7908457           0.88651519    24.0
## 786         44          0.8047439           0.89942630    24.0
## 787         32          0.8907547           0.96637633    26.0
## 788         54          0.9051673           0.97400262    26.0
## 789          8          0.7684004           0.91221213    39.0
## 790        147          0.7627852           0.89988320    39.0
## 791         18          0.7938557           0.88899508    24.0
## 792         73          0.7939260           0.88917360    24.0
## 793         66          0.8486197           0.93763660    25.0
## 794         24          0.8020632           0.89753139    24.0
## 795         31          0.8845691           0.96244620    26.0
## 796         56          0.8167431           0.90945932    25.0
## 797         17          0.8840648           0.96218520    26.0
## 798         41          0.8256103           0.91857335    25.0
## 799         69          0.8579266           0.94458902    25.0
## 800         27          0.7877416           0.93117271    40.0
## 801         17          0.7941172           0.93460147    40.0
## 802         46          0.8401240           0.93064728    25.0
## 803         47          0.8477352           0.93678377    25.0
## 804         19          0.8883486           0.96475750    26.0
## 805         62          0.8140548           0.95088802    41.0
## 806         19          0.8461908           0.93565132    25.0
## 807         60          0.8506745           0.93909260    25.0
## 808         34          0.9128407           0.97800471    27.0
## 809        106          0.8432588           0.96909761    42.0
## 810         49          0.8802905           0.95968204    26.0
## 811         74          0.8871580           0.96401924    26.0
## 812         26          0.8900523           0.96587396    26.0
## 813        235          0.8702128           0.98052253    43.0
##                    model year      full_name_winner       full_name_loser
## 1   Multi-Norm_bin_games 2013     Sergiy Stakhovsky         Roger Federer
## 2   Multi-Norm_bin_games 2013          Steve Darcis          Rafael Nadal
## 3   Multi-Norm_bin_games 2016           Sam Querrey        Novak Djokovic
## 4   Multi-Norm_bin_games 2014          Ivo Karlovic       Grigor Dimitrov
## 5   Multi-Norm_bin_games 2015           Robin Haase         Stan Wawrinka
## 6   Multi-Norm_bin_games 2015             Dudi Sela     Mikhail Kukushkin
## 7   Multi-Norm_bin_games 2014         Stan Wawrinka        Novak Djokovic
## 8   Multi-Norm_bin_games 2015          Benoit Paire         Kei Nishikori
## 9   Multi-Norm_bin_games 2016         Jurgen Melzer         Dominic Thiem
## 10  Multi-Norm_bin_games 2014        Radek Stepanek           Andy Murray
## 11  Multi-Norm_bin_games 2014          David Ferrer          Rafael Nadal
## 12  Multi-Norm_bin_games 2017          David Ferrer       Richard Gasquet
## 13  Multi-Norm_bin_games 2015          Marsel Ilhan        Jerzy Janowicz
## 14  Multi-Norm_bin_games 2013          David Ferrer          Rafael Nadal
## 15  Multi-Norm_bin_games 2014        Simone Bolelli Philipp Kohlschreiber
## 16  Multi-Norm_bin_games 2015          Gilles Simon           Andy Murray
## 17  Multi-Norm_bin_games 2015     Fernando Verdasco          Rafael Nadal
## 18  Multi-Norm_bin_games 2014        Carlos Berlocq          David Ferrer
## 19  Multi-Norm_bin_games 2014    Jo-Wilfried Tsonga        Novak Djokovic
## 20  Multi-Norm_bin_games 2015         Ryan Harrison       Grigor Dimitrov
## 21  Multi-Norm_bin_games 2014         Martin Klizan         Kei Nishikori
## 22  Multi-Norm_bin_games 2014     Marinko Matosevic           Marin Cilic
## 23  Multi-Norm_bin_games 2014     Ricardas Berankis          Milos Raonic
## 24  Multi-Norm_bin_games 2015              Go Soeda   Alexandr Dolgopolov
## 25  Multi-Norm_bin_games 2015            Rajeev Ram            John Isner
## 26  Multi-Norm_bin_games 2015           Lukas Rosol Roberto Bautista Agut
## 27  Multi-Norm_bin_games 2013            Rajeev Ram         Fabio Fognini
## 28  Multi-Norm_bin_games 2014         Stan Wawrinka          Rafael Nadal
## 29  Multi-Norm_bin_games 2014       Alejandro Falla Philipp Kohlschreiber
## 30  Multi-Norm_bin_games 2015        Viktor Troicki          Milos Raonic
## 31  Multi-Norm_bin_games 2015          Donald Young        Kevin Anderson
## 32  Multi-Norm_bin_games 2015            Mardy Fish        Viktor Troicki
## 33  Multi-Norm_bin_games 2014            Ivan Dodig            John Isner
## 34  Multi-Norm_bin_games 2015     Marcel Granollers          Gael Monfils
## 35  Multi-Norm_bin_games 2015       Feliciano Lopez         Kei Nishikori
## 36  Multi-Norm_bin_games 2014            Tommy Haas         Stan Wawrinka
## 37  Multi-Norm_bin_games 2015        Simone Bolelli          Milos Raonic
## 38  Multi-Norm_bin_games 2015     Mikhail Kukushkin       Grigor Dimitrov
## 39  Multi-Norm_bin_games 2014           Lukas Rosol         Fabio Fognini
## 40  Multi-Norm_bin_games 2014   Teymuraz Gabashvili     Sergiy Stakhovsky
## 41  Multi-Norm_bin_games 2014        Kevin Anderson         Stan Wawrinka
## 42  Multi-Norm_bin_games 2014      Thiemo De Bakker        Kevin Anderson
## 43  Multi-Norm_bin_games 2015          Benoit Paire         Kei Nishikori
## 44  Multi-Norm_bin_games 2014        Carlos Berlocq         Tomas Berdych
## 45  Multi-Norm_bin_games 2014          David Ferrer           Andy Murray
## 46  Multi-Norm_bin_games 2015          Gael Monfils         Roger Federer
## 47  Multi-Norm_bin_games 2015   Alexandr Dolgopolov          Rafael Nadal
## 48  Multi-Norm_bin_games 2014      Santiago Giraldo       Nicolas Almagro
## 49  Multi-Norm_bin_games 2014          Dustin Brown            John Isner
## 50  Multi-Norm_bin_games 2014         Jurgen Melzer           Marin Cilic
## 51  Multi-Norm_bin_games 2014           Robin Haase       Richard Gasquet
## 52  Multi-Norm_bin_games 2015          Aljaz Bedene         Jeremy Chardy
## 53  Multi-Norm_bin_games 2015         Nicolas Mahut           Sam Querrey
## 54  Multi-Norm_bin_games 2015       Benjamin Becker       Grigor Dimitrov
## 55  Multi-Norm_bin_games 2015          Benoit Paire          David Goffin
## 56  Multi-Norm_bin_games 2014         Roger Federer        Novak Djokovic
## 57  Multi-Norm_bin_games 2014          Gilles Simon          David Ferrer
## 58  Multi-Norm_bin_games 2014          Ivo Karlovic           Marin Cilic
## 59  Multi-Norm_bin_games 2014       Michael Russell        Lleyton Hewitt
## 60  Multi-Norm_bin_games 2014          Albert Ramos           Sam Querrey
## 61  Multi-Norm_bin_games 2015     Marinko Matosevic            John Isner
## 62  Multi-Norm_bin_games 2014     Marinko Matosevic Philipp Kohlschreiber
## 63  Multi-Norm_bin_games 2015   Alexandr Dolgopolov         Tomas Berdych
## 64  Multi-Norm_bin_games 2014        Jerzy Janowicz       Grigor Dimitrov
## 65  Multi-Norm_bin_games 2014      Julien Benneteau    Jo-Wilfried Tsonga
## 66  Multi-Norm_bin_games 2016           Andy Murray          Milos Raonic
## 67  Multi-Norm_bin_games 2015       Mikhail Youzhny          Gilles Simon
## 68  Multi-Norm_bin_games 2014         Andreas Seppi        Lleyton Hewitt
## 69  Multi-Norm_bin_games 2015          Aljaz Bedene Roberto Bautista Agut
## 70  Multi-Norm_bin_games 2014          Gilles Simon           Marin Cilic
## 71  Multi-Norm_bin_games 2014     Marcel Granollers   Alexandr Dolgopolov
## 72  Multi-Norm_bin_games 2014       Feliciano Lopez          Milos Raonic
## 73  Multi-Norm_bin_games 2014     Ricardas Berankis          Gilles Simon
## 74  Multi-Norm_bin_games 2014           Juan Monaco       Richard Gasquet
## 75  Multi-Norm_bin_games 2015          Marsel Ilhan       Feliciano Lopez
## 76  Multi-Norm_bin_games 2015          Benoit Paire         Fabio Fognini
## 77  Multi-Norm_bin_games 2014        Viktor Troicki          David Ferrer
## 78  Multi-Norm_bin_games 2014        Simone Bolelli        Vasek Pospisil
## 79  Multi-Norm_bin_games 2014       Mikhail Youzhny    Jo-Wilfried Tsonga
## 80  Multi-Norm_bin_games 2014          Marc Gicquel          Gilles Simon
## 81  Multi-Norm_bin_games 2015         Martin Klizan       Nicolas Almagro
## 82  Multi-Norm_bin_games 2014           Lukas Lacko         Denis Istomin
## 83  Multi-Norm_bin_games 2015         Gilles Muller       Grigor Dimitrov
## 84  Multi-Norm_bin_games 2015           Tatsuma Ito         Steve Johnson
## 85  Multi-Norm_bin_games 2015     Federico Delbonis         Stan Wawrinka
## 86  Multi-Norm_bin_games 2015        Jerzy Janowicz          Gael Monfils
## 87  Multi-Norm_bin_games 2015        Ernests Gulbis            John Isner
## 88  Multi-Norm_bin_games 2015          Lukasz Kubot        Kevin Anderson
## 89  Multi-Norm_bin_games 2014      Julien Benneteau       Grigor Dimitrov
## 90  Multi-Norm_bin_games 2014          Lukasz Kubot   Teymuraz Gabashvili
## 91  Multi-Norm_bin_games 2014         Martin Klizan         Fabio Fognini
## 92  Multi-Norm_bin_games 2014           Lukas Rosol Philipp Kohlschreiber
## 93  Multi-Norm_bin_games 2015         Roger Federer        Novak Djokovic
## 94  Multi-Norm_bin_games 2015   Teymuraz Gabashvili            John Isner
## 95  Multi-Norm_bin_games 2015           Andy Murray        Novak Djokovic
## 96  Multi-Norm_bin_games 2015     Fernando Verdasco    Jo-Wilfried Tsonga
## 97  Multi-Norm_bin_games 2015              Go Soeda      Adrian Mannarino
## 98  Multi-Norm_bin_games 2014        Carlos Berlocq          Milos Raonic
## 99  Multi-Norm_bin_games 2015          Ivo Karlovic         Tomas Berdych
## 100 Multi-Norm_bin_games 2014          Malek Jaziri     Sergiy Stakhovsky
## 101 Multi-Norm_bin_games 2015    Jo-Wilfried Tsonga         Kei Nishikori
## 102 Multi-Norm_bin_games 2014      Julien Benneteau         Stan Wawrinka
## 103 Multi-Norm_bin_games 2015      Marcos Baghdatis          David Ferrer
## 104 Multi-Norm_bin_games 2014          Gilles Simon         Tomas Berdych
## 105 Multi-Norm_bin_games 2014         Nicolas Mahut         Tommy Robredo
## 106 Multi-Norm_bin_games 2015        Vasek Pospisil        Viktor Troicki
## 107 Multi-Norm_bin_games 2014         Roger Federer        Novak Djokovic
## 108 Multi-Norm_bin_games 2014     Mikhail Kukushkin         Tommy Robredo
## 109 Multi-Norm_bin_games 2014         Pablo Andujar         Tommy Robredo
## 110 Multi-Norm_bin_games 2014         Paolo Lorenzi         Pablo Andujar
## 111 Multi-Norm_bin_games 2015          Gilles Simon          Milos Raonic
## 112 Multi-Norm_bin_games 2014    Matthias Bachinger        Leonardo Mayer
## 113 Multi-Norm_bin_games 2015         Gilles Muller         Bernard Tomic
## 114 Multi-Norm_bin_games 2015          Benoit Paire Philipp Kohlschreiber
## 115 Multi-Norm_bin_games 2014        Victor Hanescu        Kevin Anderson
## 116 Multi-Norm_bin_games 2014        Leonardo Mayer         Andreas Seppi
## 117 Multi-Norm_bin_games 2014          Tobias Kamke   Alexandr Dolgopolov
## 118 Multi-Norm_bin_games 2014      Julien Benneteau        Ernests Gulbis
## 119 Multi-Norm_bin_games 2014         Roger Federer        Novak Djokovic
## 120 Multi-Norm_bin_games 2015       Benjamin Becker         Jeremy Chardy
## 121 Multi-Norm_bin_games 2014      Julien Benneteau        Ernests Gulbis
## 122 Multi-Norm_bin_games 2014     Sergiy Stakhovsky        Ernests Gulbis
## 123 Multi-Norm_bin_games 2015       Feliciano Lopez          Milos Raonic
## 124 Multi-Norm_bin_games 2015       Mikhail Youzhny        Viktor Troicki
## 125 Multi-Norm_bin_games 2014     Ricardas Berankis         Jurgen Melzer
## 126 Multi-Norm_bin_games 2015        Simone Bolelli          David Goffin
## 127 Multi-Norm_bin_games 2015            John Isner         Kei Nishikori
## 128 Multi-Norm_bin_games 2015         Florian Mayer       Mikhail Youzhny
## 129 Multi-Norm_bin_games 2015       Thomaz Bellucci Roberto Bautista Agut
## 130 Multi-Norm_bin_games 2015      Santiago Giraldo           Marin Cilic
## 131 Multi-Norm_bin_games 2015         Jurgen Melzer      Adrian Mannarino
## 132 Multi-Norm_bin_games 2015         Gilles Muller       Grigor Dimitrov
## 133 Multi-Norm_bin_games 2015          Marsel Ilhan      Andrey Kuznetsov
## 134 Multi-Norm_bin_games 2015    Jo-Wilfried Tsonga          Rafael Nadal
## 135 Multi-Norm_bin_games 2014      Santiago Giraldo         Tommy Robredo
## 136 Multi-Norm_bin_games 2015        Kevin Anderson         Stan Wawrinka
## 137 Multi-Norm_bin_games 2015     Marcel Granollers            Ivan Dodig
## 138 Multi-Norm_bin_games 2014     Fernando Verdasco       Richard Gasquet
## 139 Multi-Norm_bin_games 2014   Alexandr Dolgopolov         Stan Wawrinka
## 140 Multi-Norm_bin_games 2014       Jarkko Nieminen       Dmitry Tursunov
## 141 Multi-Norm_bin_games 2015           Juan Monaco         Florian Mayer
## 142 Multi-Norm_bin_games 2015         Steve Johnson        Kevin Anderson
## 143 Multi-Norm_bin_games 2014         Andreas Seppi        Radek Stepanek
## 144 Multi-Norm_bin_games 2015   Alexandr Dolgopolov           Jiri Vesely
## 145 Multi-Norm_bin_games 2015         Bernard Tomic       Richard Gasquet
## 146 Multi-Norm_bin_games 2015        Viktor Troicki             Jack Sock
## 147 Multi-Norm_bin_games 2014      Marcos Baghdatis Philipp Kohlschreiber
## 148 Multi-Norm_bin_games 2014         Matthew Ebden      Adrian Mannarino
## 149 Multi-Norm_bin_games 2014         Robby Ginepri     Sergiy Stakhovsky
## 150 Multi-Norm_bin_games 2014        Kevin Anderson         Stan Wawrinka
## 151 Multi-Norm_bin_games 2015              Go Soeda    Matthias Bachinger
## 152 Multi-Norm_bin_games 2015         Tommy Robredo       Grigor Dimitrov
## 153 Multi-Norm_bin_games 2014     Marcel Granollers         Martin Klizan
## 154 Multi-Norm_bin_games 2014        Leonardo Mayer Philipp Kohlschreiber
## 155 Multi-Norm_bin_games 2015          Dustin Brown           Sam Querrey
## 156 Multi-Norm_bin_games 2015          Benoit Paire          Pablo Cuevas
## 157 Multi-Norm_bin_games 2013         Jurgen Melzer         Fabio Fognini
## 158 Multi-Norm_bin_games 2014        Leonardo Mayer         Tommy Robredo
## 159 Multi-Norm_bin_games 2014           Robin Haase       Mikhail Youzhny
## 160 Multi-Norm_bin_games 2014   Teymuraz Gabashvili      Santiago Giraldo
## 161 Multi-Norm_bin_games 2015            Joao Sousa         Gilles Muller
## 162 Multi-Norm_bin_games 2015     Marco Chiudinelli          Benoit Paire
## 163 Multi-Norm_bin_games 2014       Benjamin Becker         Ryan Harrison
## 164 Multi-Norm_bin_games 2014             Pere Riba         Paolo Lorenzi
## 165 Multi-Norm_bin_games 2014         Jeremy Chardy        Kevin Anderson
## 166 Multi-Norm_bin_games 2015         Pablo Andujar Philipp Kohlschreiber
## 167 Multi-Norm_bin_games 2015    Jo-Wilfried Tsonga         Tomas Berdych
## 168 Multi-Norm_bin_games 2015          Malek Jaziri       Thomaz Bellucci
## 169 Multi-Norm_bin_games 2015         Roger Federer        Novak Djokovic
## 170 Multi-Norm_bin_games 2014            Bjorn Phau             Dudi Sela
## 171 Multi-Norm_bin_games 2014       Benjamin Becker          Ivo Karlovic
## 172 Multi-Norm_bin_games 2015      Marcos Baghdatis          David Goffin
## 173 Multi-Norm_bin_games 2014     Sergiy Stakhovsky            Ivan Dodig
## 174 Multi-Norm_bin_games 2014     Marcel Granollers         Nicolas Mahut
## 175 Multi-Norm_bin_games 2014          Malek Jaziri          Donald Young
## 176 Multi-Norm_bin_games 2015        Radek Stepanek            Ivan Dodig
## 177 Multi-Norm_bin_games 2015        Kevin Anderson         Kei Nishikori
## 178 Multi-Norm_bin_games 2015          Malek Jaziri   Teymuraz Gabashvili
## 179 Multi-Norm_bin_games 2014          Gilles Simon         Daniel Brands
## 180 Multi-Norm_bin_games 2015       Albert Montanes      Santiago Giraldo
## 181 Multi-Norm_bin_games 2015         Jurgen Melzer         Ryan Harrison
## 182 Multi-Norm_bin_games 2015           Juan Monaco           Marin Cilic
## 183 Multi-Norm_bin_games 2014           Lukas Rosol       Dmitry Tursunov
## 184 Multi-Norm_bin_games 2014       Albert Montanes   Alexandr Dolgopolov
## 185 Multi-Norm_bin_games 2014      Adrian Mannarino         Fabio Fognini
## 186 Multi-Norm_bin_games 2014   Alexandr Dolgopolov          Gilles Simon
## 187 Multi-Norm_bin_games 2015         Martin Klizan         Tommy Robredo
## 188 Multi-Norm_bin_games 2015          Pablo Cuevas       Grigor Dimitrov
## 189 Multi-Norm_bin_games 2015       Illya Marchenko            Joao Sousa
## 190 Multi-Norm_bin_games 2015         Denis Istomin           Sam Querrey
## 191 Multi-Norm_bin_games 2015         Fabio Fognini         Steve Johnson
## 192 Multi-Norm_bin_games 2015         Jurgen Melzer           Denis Kudla
## 193 Multi-Norm_bin_games 2015         Denis Istomin     Mikhail Kukushkin
## 194 Multi-Norm_bin_games 2015          Ivo Karlovic          Milos Raonic
## 195 Multi-Norm_bin_games 2014         Tommy Robredo           Marin Cilic
## 196 Multi-Norm_bin_games 2014      Julien Benneteau        Lleyton Hewitt
## 197 Multi-Norm_bin_games 2014           Blaz Kavcic          Donald Young
## 198 Multi-Norm_bin_games 2015      Marcos Baghdatis          Steve Darcis
## 199 Multi-Norm_bin_games 2015           Rui Machado            Joao Sousa
## 200 Multi-Norm_bin_games 2014       Albert Montanes           Robin Haase
## 201 Multi-Norm_bin_games 2014           Robin Haase          Benoit Paire
## 202 Multi-Norm_bin_games 2015         Gilles Muller         Jeremy Chardy
## 203 Multi-Norm_bin_games 2015           Marin Cilic    Jo-Wilfried Tsonga
## 204 Multi-Norm_bin_games 2015        Ernests Gulbis   Alexandr Dolgopolov
## 205 Multi-Norm_bin_games 2014       Stephane Robert     Michal Przysiezny
## 206 Multi-Norm_bin_games 2014           Sam Querrey        Ernests Gulbis
## 207 Multi-Norm_bin_games 2015          David Ferrer         Tomas Berdych
## 208 Multi-Norm_bin_games 2014     Nikolay Davydenko      Julien Benneteau
## 209 Multi-Norm_bin_games 2014     Fernando Verdasco          Gilles Simon
## 210 Multi-Norm_bin_games 2014       Feliciano Lopez Roberto Bautista Agut
## 211 Multi-Norm_bin_games 2015          David Ferrer         Kei Nishikori
## 212 Multi-Norm_bin_games 2015     Ricardas Berankis         Steve Johnson
## 213 Multi-Norm_bin_games 2014        Kevin Anderson   Alexandr Dolgopolov
## 214 Multi-Norm_bin_games 2014            Tommy Haas         Kei Nishikori
## 215 Multi-Norm_bin_games 2014          Benoit Paire       Albert Montanes
## 216 Multi-Norm_bin_games 2014             Dudi Sela      Adrian Mannarino
## 217 Multi-Norm_bin_games 2014         Denis Istomin         Bernard Tomic
## 218 Multi-Norm_bin_games 2015         Andreas Seppi         Jeremy Chardy
## 219 Multi-Norm_bin_games 2015         Gilles Muller          David Goffin
## 220 Multi-Norm_bin_games 2015         Jeremy Chardy            John Isner
## 221 Multi-Norm_bin_games 2015       Richard Gasquet         Stan Wawrinka
## 222 Multi-Norm_bin_games 2015          Benoit Paire         Gilles Muller
## 223 Multi-Norm_bin_games 2015       Benjamin Becker        Andrey Golubev
## 224 Multi-Norm_bin_games 2014           Robin Haase        Carlos Berlocq
## 225 Multi-Norm_bin_games 2014         Andreas Seppi      Santiago Giraldo
## 226 Multi-Norm_bin_games 2015        Jerzy Janowicz          Gilles Simon
## 227 Multi-Norm_bin_games 2014     Alex Bogomolov Jr         Ryan Harrison
## 228 Multi-Norm_bin_games 2014         Andreas Seppi         Florian Mayer
## 229 Multi-Norm_bin_games 2014       Alejandro Falla       Jarkko Nieminen
## 230 Multi-Norm_bin_games 2014            John Isner         Tommy Robredo
## 231 Multi-Norm_bin_games 2014      Julien Benneteau        Ernests Gulbis
## 232 Multi-Norm_bin_games 2014       Mikhail Youzhny        Ernests Gulbis
## 233 Multi-Norm_bin_games 2015          Milos Raonic         Kei Nishikori
## 234 Multi-Norm_bin_games 2015     Ricardas Berankis         Gilles Muller
## 235 Multi-Norm_bin_games 2015         Martin Klizan       Thomaz Bellucci
## 236 Multi-Norm_bin_games 2015           Lukas Rosol         Martin Klizan
## 237 Multi-Norm_bin_games 2015           Juan Monaco       Nicolas Almagro
## 238 Multi-Norm_bin_games 2014     Fernando Verdasco       Nicolas Almagro
## 239 Multi-Norm_bin_games 2015       Alejandro Falla            Joao Souza
## 240 Multi-Norm_bin_games 2014          Ivo Karlovic            John Isner
## 241 Multi-Norm_bin_games 2015          Rafael Nadal           Andy Murray
## 242 Multi-Norm_bin_games 2015        Simone Bolelli     Marinko Matosevic
## 243 Multi-Norm_bin_games 2015      Julien Benneteau        Vasek Pospisil
## 244 Multi-Norm_bin_games 2015       Thomaz Bellucci          Pablo Cuevas
## 245 Multi-Norm_bin_games 2015          Dustin Brown      Andrey Kuznetsov
## 246 Multi-Norm_bin_games 2015     Sergiy Stakhovsky        Viktor Troicki
## 247 Multi-Norm_bin_games 2015 Roberto Bautista Agut       Richard Gasquet
## 248 Multi-Norm_bin_games 2015        Ernests Gulbis          Ivo Karlovic
## 249 Multi-Norm_bin_games 2014       Jarkko Nieminen           Robin Haase
## 250 Multi-Norm_bin_games 2014       Feliciano Lopez           Sam Querrey
## 251 Multi-Norm_bin_games 2014   Alexandr Dolgopolov         Fabio Fognini
## 252 Multi-Norm_bin_games 2014      Horacio Zeballos          Pablo Cuevas
## 253 Multi-Norm_bin_games 2014           Robin Haase       Mikhail Youzhny
## 254 Multi-Norm_bin_games 2014         Jurgen Melzer     Fernando Verdasco
## 255 Multi-Norm_bin_games 2014          Malek Jaziri     Ricardas Berankis
## 256 Multi-Norm_bin_games 2015         Pablo Andujar         Fabio Fognini
## 257 Multi-Norm_bin_games 2015         Martin Klizan        Vasek Pospisil
## 258 Multi-Norm_bin_games 2014         Jurgen Melzer            John Isner
## 259 Multi-Norm_bin_games 2014           Marin Cilic    Jo-Wilfried Tsonga
## 260 Multi-Norm_bin_games 2014        Jerzy Janowicz          David Goffin
## 261 Multi-Norm_bin_games 2015          Gilles Simon          Gael Monfils
## 262 Multi-Norm_bin_games 2015       Richard Gasquet       Nicolas Almagro
## 263 Multi-Norm_bin_games 2014 Philipp Kohlschreiber         Tommy Robredo
## 264 Multi-Norm_bin_games 2014 Philipp Kohlschreiber            John Isner
## 265 Multi-Norm_bin_games 2014         Andreas Seppi        Simone Bolelli
## 266 Multi-Norm_bin_games 2014       Michael Russell     Michal Przysiezny
## 267 Multi-Norm_bin_games 2014           Lukas Rosol         Daniel Brands
## 268 Multi-Norm_bin_games 2014       Stephane Robert     Alex Bogomolov Jr
## 269 Multi-Norm_bin_games 2014          Pablo Cuevas         Jeremy Chardy
## 270 Multi-Norm_bin_games 2015       Feliciano Lopez        Jerzy Janowicz
## 271 Multi-Norm_bin_games 2015            John Isner          Milos Raonic
## 272 Multi-Norm_bin_games 2015         Jeremy Chardy          David Goffin
## 273 Multi-Norm_bin_games 2015           Sam Querrey            John Isner
## 274 Multi-Norm_bin_games 2015        Evgeny Donskoy   Teymuraz Gabashvili
## 275 Multi-Norm_bin_games 2015         Steve Johnson             Jack Sock
## 276 Multi-Norm_bin_games 2014             Dudi Sela           Lukas Rosol
## 277 Multi-Norm_bin_games 2014        Radek Stepanek         Denis Istomin
## 278 Multi-Norm_bin_games 2014         Jeremy Chardy           Lukas Rosol
## 279 Multi-Norm_bin_games 2014      Julien Benneteau          Gilles Simon
## 280 Multi-Norm_bin_games 2014           Juan Monaco        Vasek Pospisil
## 281 Multi-Norm_bin_games 2015      Marcos Baghdatis          Ivo Karlovic
## 282 Multi-Norm_bin_games 2015        Ernests Gulbis     Sergiy Stakhovsky
## 283 Multi-Norm_bin_games 2015          Steve Darcis      Adrian Mannarino
## 284 Multi-Norm_bin_games 2015         Mischa Zverev         Fabio Fognini
## 285 Multi-Norm_bin_games 2015        Jerzy Janowicz Roberto Bautista Agut
## 286 Multi-Norm_bin_games 2014        Ernests Gulbis       Grigor Dimitrov
## 287 Multi-Norm_bin_games 2014         Nicolas Mahut           Blaz Kavcic
## 288 Multi-Norm_bin_games 2015         Nicolas Mahut Roberto Bautista Agut
## 289 Multi-Norm_bin_games 2015           Jan Hernych       Alejandro Falla
## 290 Multi-Norm_bin_games 2014          Ivo Karlovic         Bernard Tomic
## 291 Multi-Norm_bin_games 2015           Marin Cilic    Jo-Wilfried Tsonga
## 292 Multi-Norm_bin_games 2015           Sam Querrey   Alexandr Dolgopolov
## 293 Multi-Norm_bin_games 2015           Andy Murray         Kei Nishikori
## 294 Multi-Norm_bin_games 2014       Dmitry Tursunov         Denis Istomin
## 295 Multi-Norm_bin_games 2014     Mikhail Kukushkin        Frank Dancevic
## 296 Multi-Norm_bin_games 2014         Denis Istomin        Jerzy Janowicz
## 297 Multi-Norm_bin_games 2015          Donald Young      Adrian Mannarino
## 298 Multi-Norm_bin_games 2015     Sergiy Stakhovsky     Marcel Granollers
## 299 Multi-Norm_bin_games 2015     Marinko Matosevic     Marcel Granollers
## 300 Multi-Norm_bin_games 2015        Carlos Berlocq         Fabio Fognini
## 301 Multi-Norm_bin_games 2015          Steve Darcis         Gilles Muller
## 302 Multi-Norm_bin_games 2015     Marcel Granollers      Adrian Mannarino
## 303 Multi-Norm_bin_games 2015   Alexandr Dolgopolov         Bernard Tomic
## 304 Multi-Norm_bin_games 2014             Dudi Sela          Benoit Paire
## 305 Multi-Norm_bin_games 2014             Dudi Sela          Donald Young
## 306 Multi-Norm_bin_games 2015         Igor Sijsling      Adrian Mannarino
## 307 Multi-Norm_bin_games 2015          Gael Monfils Philipp Kohlschreiber
## 308 Multi-Norm_bin_games 2015        Vasek Pospisil         Fabio Fognini
## 309 Multi-Norm_bin_games 2015           Robin Haase          Pablo Cuevas
## 310 Multi-Norm_bin_games 2014       Thomaz Bellucci            Ivan Dodig
## 311 Multi-Norm_bin_games 2015      Santiago Giraldo           Robin Haase
## 312 Multi-Norm_bin_games 2014         Pablo Andujar     Marcel Granollers
## 313 Multi-Norm_bin_games 2014       Benjamin Becker           Lukas Lacko
## 314 Multi-Norm_bin_games 2014          Albert Ramos        Leonardo Mayer
## 315 Multi-Norm_bin_games 2014           Marin Cilic         Tommy Robredo
## 316 Multi-Norm_bin_games 2014         Andreas Seppi          Albert Ramos
## 317 Multi-Norm_bin_games 2014       Alejandro Falla           Robin Haase
## 318 Multi-Norm_bin_games 2014          Gilles Simon         Bernard Tomic
## 319 Multi-Norm_bin_games 2014        Andrey Golubev   Teymuraz Gabashvili
## 320 Multi-Norm_bin_games 2015     Marcel Granollers       Stephane Robert
## 321 Multi-Norm_bin_games 2015         Stan Wawrinka         Kei Nishikori
## 322 Multi-Norm_bin_games 2015          Dustin Brown     Marinko Matosevic
## 323 Multi-Norm_bin_games 2015            John Isner       Grigor Dimitrov
## 324 Multi-Norm_bin_games 2015           Sam Querrey          Gilles Simon
## 325 Multi-Norm_bin_games 2015      Marcos Baghdatis         Gilles Muller
## 326 Multi-Norm_bin_games 2015         Andreas Seppi       Benjamin Becker
## 327 Multi-Norm_bin_games 2015          Benoit Paire         Denis Istomin
## 328 Multi-Norm_bin_games 2015      Marcos Baghdatis         Gilles Muller
## 329 Multi-Norm_bin_games 2014            John Isner        Ernests Gulbis
## 330 Multi-Norm_bin_games 2014       Albert Montanes     Michal Przysiezny
## 331 Multi-Norm_bin_games 2014        Radek Stepanek         Pablo Andujar
## 332 Multi-Norm_bin_games 2014          Ivo Karlovic          Tobias Kamke
## 333 Multi-Norm_bin_games 2014        Victor Hanescu         Pablo Andujar
## 334 Multi-Norm_bin_games 2015           Robin Haase       Feliciano Lopez
## 335 Multi-Norm_bin_games 2015      Marcos Baghdatis         Bernard Tomic
## 336 Multi-Norm_bin_games 2014   Teymuraz Gabashvili         Matthew Ebden
## 337 Multi-Norm_bin_games 2014           Sam Querrey        Kevin Anderson
## 338 Multi-Norm_bin_games 2014    Jo-Wilfried Tsonga         Fabio Fognini
## 339 Multi-Norm_bin_games 2014          Gael Monfils       Grigor Dimitrov
## 340 Multi-Norm_bin_games 2014       Michael Russell          Donald Young
## 341 Multi-Norm_bin_games 2015     Ricardas Berankis           Lukas Lacko
## 342 Multi-Norm_bin_games 2015      Janko Tipsarevic         Bernard Tomic
## 343 Multi-Norm_bin_games 2015           Jiri Vesely         Martin Klizan
## 344 Multi-Norm_bin_games 2015       Richard Gasquet       Grigor Dimitrov
## 345 Multi-Norm_bin_games 2014            John Isner Philipp Kohlschreiber
## 346 Multi-Norm_bin_games 2014         Florian Mayer            Ivan Dodig
## 347 Multi-Norm_bin_games 2014          Milos Raonic         Tommy Robredo
## 348 Multi-Norm_bin_games 2014       Mikhail Youzhny        Leonardo Mayer
## 349 Multi-Norm_bin_games 2014         Nicolas Mahut         Daniel Brands
## 350 Multi-Norm_bin_games 2014     Fernando Verdasco       Richard Gasquet
## 351 Multi-Norm_bin_games 2014          Benoit Paire        Andrey Golubev
## 352 Multi-Norm_bin_games 2014             Dudi Sela       Benjamin Becker
## 353 Multi-Norm_bin_games 2014         Tomas Berdych           Marin Cilic
## 354 Multi-Norm_bin_games 2015        Viktor Troicki       Feliciano Lopez
## 355 Multi-Norm_bin_games 2015         Tomas Berdych    Jo-Wilfried Tsonga
## 356 Multi-Norm_bin_games 2015        Viktor Troicki       Feliciano Lopez
## 357 Multi-Norm_bin_games 2015         Nicolas Mahut          David Goffin
## 358 Multi-Norm_bin_games 2015            John Isner       Feliciano Lopez
## 359 Multi-Norm_bin_games 2015         Denis Istomin          Donald Young
## 360 Multi-Norm_bin_games 2015      Marcos Baghdatis           Sam Querrey
## 361 Multi-Norm_bin_games 2014         Denis Istomin       Dmitry Tursunov
## 362 Multi-Norm_bin_games 2014    Matthias Bachinger      Adrian Mannarino
## 363 Multi-Norm_bin_games 2015           Juan Monaco        Leonardo Mayer
## 364 Multi-Norm_bin_games 2014          Ivo Karlovic       Feliciano Lopez
## 365 Multi-Norm_bin_games 2014           Juan Monaco          Albert Ramos
## 366 Multi-Norm_bin_games 2014         Jeremy Chardy     Marinko Matosevic
## 367 Multi-Norm_bin_games 2014          Tobias Kamke        Simone Bolelli
## 368 Multi-Norm_bin_games 2015        Viktor Troicki        Simone Bolelli
## 369 Multi-Norm_bin_games 2015         Andreas Seppi         Martin Klizan
## 370 Multi-Norm_bin_games 2015       Nicolas Almagro       Jarkko Nieminen
## 371 Multi-Norm_bin_games 2015       Mikhail Youzhny     Sergiy Stakhovsky
## 372 Multi-Norm_bin_games 2014         Jeremy Chardy            Ivan Dodig
## 373 Multi-Norm_bin_games 2014       Richard Gasquet         Kei Nishikori
## 374 Multi-Norm_bin_games 2015         Andreas Seppi        Leonardo Mayer
## 375 Multi-Norm_bin_games 2015         Andreas Seppi      Adrian Mannarino
## 376 Multi-Norm_bin_games 2015          Marsel Ilhan           Tatsuma Ito
## 377 Multi-Norm_bin_games 2014          Gilles Simon        Carlos Berlocq
## 378 Multi-Norm_bin_games 2015      Marcos Baghdatis          Ivo Karlovic
## 379 Multi-Norm_bin_games 2015         Florian Mayer       Albert Montanes
## 380 Multi-Norm_bin_games 2014         Nicolas Mahut         Ryan Harrison
## 381 Multi-Norm_bin_games 2014      Santiago Giraldo     Marcel Granollers
## 382 Multi-Norm_bin_games 2014       Thomaz Bellucci      Santiago Giraldo
## 383 Multi-Norm_bin_games 2014         Martin Klizan     Marcel Granollers
## 384 Multi-Norm_bin_games 2014      Marcos Baghdatis      Santiago Giraldo
## 385 Multi-Norm_bin_games 2014         Kei Nishikori       Grigor Dimitrov
## 386 Multi-Norm_bin_games 2014          Gael Monfils         Fabio Fognini
## 387 Multi-Norm_bin_games 2014         Martin Klizan          Donald Young
## 388 Multi-Norm_bin_games 2014         Igor Sijsling        Andrey Golubev
## 389 Multi-Norm_bin_games 2014     Fernando Verdasco       Jarkko Nieminen
## 390 Multi-Norm_bin_games 2014         Tommy Robredo        Vasek Pospisil
## 391 Multi-Norm_bin_games 2015        Viktor Troicki     Mikhail Kukushkin
## 392 Multi-Norm_bin_games 2015             Dudi Sela           Lukas Rosol
## 393 Multi-Norm_bin_games 2015           Juan Monaco          Pablo Cuevas
## 394 Multi-Norm_bin_games 2015         Jurgen Melzer     Kenny De Schepper
## 395 Multi-Norm_bin_games 2015        Jerzy Janowicz          Dustin Brown
## 396 Multi-Norm_bin_games 2015          Ivo Karlovic   Alexandr Dolgopolov
## 397 Multi-Norm_bin_games 2015       Nicolas Almagro     Fernando Verdasco
## 398 Multi-Norm_bin_games 2015       Jarkko Nieminen    Matthias Bachinger
## 399 Multi-Norm_bin_games 2015     Ricardas Berankis   Teymuraz Gabashvili
## 400 Multi-Norm_bin_games 2014             Dudi Sela           Lukas Lacko
## 401 Multi-Norm_bin_games 2015          Marsel Ilhan      Adrian Mannarino
## 402 Multi-Norm_bin_games 2015     Ricardas Berankis            Joao Sousa
## 403 Multi-Norm_bin_games 2014          Dustin Brown   Teymuraz Gabashvili
## 404 Multi-Norm_bin_games 2014         Jurgen Melzer     Mikhail Kukushkin
## 405 Multi-Norm_bin_games 2014            Tommy Haas         Andreas Seppi
## 406 Multi-Norm_bin_games 2014      Santiago Giraldo       Benjamin Becker
## 407 Multi-Norm_bin_games 2014           Marin Cilic         Kei Nishikori
## 408 Multi-Norm_bin_games 2015     Fernando Verdasco Roberto Bautista Agut
## 409 Multi-Norm_bin_games 2015           Robin Haase       Alejandro Falla
## 410 Multi-Norm_bin_games 2014            Tommy Haas         Jeremy Chardy
## 411 Multi-Norm_bin_games 2014        Ernests Gulbis   Alexandr Dolgopolov
## 412 Multi-Norm_bin_games 2014       Jarkko Nieminen        Leonardo Mayer
## 413 Multi-Norm_bin_games 2015       Jarkko Nieminen          Marsel Ilhan
## 414 Multi-Norm_bin_games 2014         Denis Istomin          Adrian Ungur
## 415 Multi-Norm_bin_games 2014        Lleyton Hewitt     Marinko Matosevic
## 416 Multi-Norm_bin_games 2014         Pablo Andujar     Marcel Granollers
## 417 Multi-Norm_bin_games 2014        Victor Hanescu       Stephane Robert
## 418 Multi-Norm_bin_games 2014           Lukas Rosol        Michael Llodra
## 419 Multi-Norm_bin_games 2014           Andy Murray       Nicolas Almagro
## 420 Multi-Norm_bin_games 2014    Jo-Wilfried Tsonga   Alexandr Dolgopolov
## 421 Multi-Norm_bin_games 2014       Albert Montanes        Leonardo Mayer
## 422 Multi-Norm_bin_games 2014       Benjamin Becker        Vasek Pospisil
## 423 Multi-Norm_bin_games 2015       Albert Montanes       Maximo Gonzalez
## 424 Multi-Norm_bin_games 2015         Tomas Berdych          Gael Monfils
## 425 Multi-Norm_bin_games 2015           Sam Querrey   Alexandr Dolgopolov
## 426 Multi-Norm_bin_games 2015        Novak Djokovic         Roger Federer
## 427 Multi-Norm_bin_games 2015      Marcos Baghdatis        Ernests Gulbis
## 428 Multi-Norm_bin_games 2015          Ivo Karlovic         Jeremy Chardy
## 429 Multi-Norm_bin_games 2014          Milos Raonic         Kei Nishikori
## 430 Multi-Norm_bin_games 2014         Tommy Robredo           Lukas Rosol
## 431 Multi-Norm_bin_games 2015         Roger Federer       Jarkko Nieminen
## 432 Multi-Norm_bin_games 2015         Gilles Muller         Paolo Lorenzi
## 433 Multi-Norm_bin_games 2014       Albert Montanes          Benoit Paire
## 434 Multi-Norm_bin_games 2014       Jarkko Nieminen   Teymuraz Gabashvili
## 435 Multi-Norm_bin_games 2014          Ivo Karlovic         Daniel Brands
## 436 Multi-Norm_bin_games 2014          Albert Ramos       Jarkko Nieminen
## 437 Multi-Norm_bin_games 2014          Gilles Simon        Victor Hanescu
## 438 Multi-Norm_bin_games 2014           Sam Querrey      Julien Benneteau
## 439 Multi-Norm_bin_games 2014     Fernando Verdasco     Marinko Matosevic
## 440 Multi-Norm_bin_games 2015    Jo-Wilfried Tsonga          David Goffin
## 441 Multi-Norm_bin_games 2015          Gael Monfils       Grigor Dimitrov
## 442 Multi-Norm_bin_games 2015            John Isner        Vasek Pospisil
## 443 Multi-Norm_bin_games 2015        Viktor Troicki         Martin Klizan
## 444 Multi-Norm_bin_games 2015        Viktor Troicki        Simone Bolelli
## 445 Multi-Norm_bin_games 2014         Andreas Seppi      Santiago Giraldo
## 446 Multi-Norm_bin_games 2014         Roger Federer           Andy Murray
## 447 Multi-Norm_bin_games 2015          Dustin Brown            Rajeev Ram
## 448 Multi-Norm_bin_games 2014       Jarkko Nieminen       Benjamin Becker
## 449 Multi-Norm_bin_games 2015       Jarkko Nieminen      Thiemo De Bakker
## 450 Multi-Norm_bin_games 2014       Jarkko Nieminen      Santiago Giraldo
## 451 Multi-Norm_bin_games 2014 Philipp Kohlschreiber         Jeremy Chardy
## 452 Multi-Norm_bin_games 2014         Martin Klizan          Steve Darcis
## 453 Multi-Norm_bin_games 2015        Viktor Troicki         Gilles Muller
## 454 Multi-Norm_bin_games 2015          Malek Jaziri           Tatsuma Ito
## 455 Multi-Norm_bin_games 2015       Feliciano Lopez         Fabio Fognini
## 456 Multi-Norm_bin_games 2015        Vasek Pospisil        Simone Bolelli
## 457 Multi-Norm_bin_games 2015        Kevin Anderson             Jack Sock
## 458 Multi-Norm_bin_games 2014           Sam Querrey         Jeremy Chardy
## 459 Multi-Norm_bin_games 2014       Mikhail Youzhny           Juan Monaco
## 460 Multi-Norm_bin_games 2014     Fernando Verdasco          Donald Young
## 461 Multi-Norm_bin_games 2015        Ernests Gulbis          Donald Young
## 462 Multi-Norm_bin_games 2015          Rafael Nadal         Stan Wawrinka
## 463 Multi-Norm_bin_games 2015         Denis Istomin             Dudi Sela
## 464 Multi-Norm_bin_games 2014           Lukas Lacko         Matthew Ebden
## 465 Multi-Norm_bin_games 2014 Roberto Bautista Agut        Vasek Pospisil
## 466 Multi-Norm_bin_games 2014       Jarkko Nieminen         Daniel Brands
## 467 Multi-Norm_bin_games 2014       Richard Gasquet        Kevin Anderson
## 468 Multi-Norm_bin_games 2014        Radek Stepanek        Kevin Anderson
## 469 Multi-Norm_bin_games 2014    Jo-Wilfried Tsonga       Grigor Dimitrov
## 470 Multi-Norm_bin_games 2015       Thomaz Bellucci   Teymuraz Gabashvili
## 471 Multi-Norm_bin_games 2015         Igor Sijsling        Frank Dancevic
## 472 Multi-Norm_bin_games 2015         Denis Istomin        Leonardo Mayer
## 473 Multi-Norm_bin_games 2014       Mikhail Youzhny            Ivan Dodig
## 474 Multi-Norm_bin_games 2015         Bernard Tomic         Fabio Fognini
## 475 Multi-Norm_bin_games 2015       Nicolas Almagro           Jiri Vesely
## 476 Multi-Norm_bin_games 2015    Jo-Wilfried Tsonga        Kevin Anderson
## 477 Multi-Norm_bin_games 2014         Tommy Robredo      Adrian Mannarino
## 478 Multi-Norm_bin_games 2014        Jerzy Janowicz   Teymuraz Gabashvili
## 479 Multi-Norm_bin_games 2014           Andy Murray           Marin Cilic
## 480 Multi-Norm_bin_games 2015         Andreas Seppi          Pablo Cuevas
## 481 Multi-Norm_bin_games 2015        Viktor Troicki         Bernard Tomic
## 482 Multi-Norm_bin_games 2015          Gilles Simon          David Goffin
## 483 Multi-Norm_bin_games 2015      Marcos Baghdatis        Vasek Pospisil
## 484 Multi-Norm_bin_games 2014     Fernando Verdasco          Albert Ramos
## 485 Multi-Norm_bin_games 2015 Philipp Kohlschreiber         Fabio Fognini
## 486 Multi-Norm_bin_games 2014            John Isner   Teymuraz Gabashvili
## 487 Multi-Norm_bin_games 2014         Jurgen Melzer       Alejandro Falla
## 488 Multi-Norm_bin_games 2014             Dudi Sela     Michal Przysiezny
## 489 Multi-Norm_bin_games 2014           Juan Monaco         Andreas Seppi
## 490 Multi-Norm_bin_games 2014       Benjamin Becker           Blaz Kavcic
## 491 Multi-Norm_bin_games 2014           Andy Murray    Jo-Wilfried Tsonga
## 492 Multi-Norm_bin_games 2014         Tomas Berdych       Grigor Dimitrov
## 493 Multi-Norm_bin_games 2015        Viktor Troicki        Leonardo Mayer
## 494 Multi-Norm_bin_games 2015             Dudi Sela           Jurgen Zopp
## 495 Multi-Norm_bin_games 2015       Richard Gasquet Roberto Bautista Agut
## 496 Multi-Norm_bin_games 2015       Nicolas Almagro     Sergiy Stakhovsky
## 497 Multi-Norm_bin_games 2015           Marin Cilic            John Isner
## 498 Multi-Norm_bin_games 2015         Tommy Robredo         Andreas Seppi
## 499 Multi-Norm_bin_games 2015       Albert Montanes     Ricardas Berankis
## 500 Multi-Norm_bin_games 2015          Rafael Nadal           Marin Cilic
## 501 Multi-Norm_bin_games 2014       Richard Gasquet         Bernard Tomic
## 502 Multi-Norm_bin_games 2015       Feliciano Lopez          Pablo Cuevas
## 503 Multi-Norm_bin_games 2015           Juan Monaco     Federico Delbonis
## 504 Multi-Norm_bin_games 2014      Julien Benneteau         Matthew Ebden
## 505 Multi-Norm_bin_games 2014         Roger Federer         Tomas Berdych
## 506 Multi-Norm_bin_games 2014       Feliciano Lopez         Jeremy Chardy
## 507 Multi-Norm_bin_games 2014      Marcos Baghdatis          Dustin Brown
## 508 Multi-Norm_bin_games 2014           Juan Monaco       Thomaz Bellucci
## 509 Multi-Norm_bin_games 2015          Ivo Karlovic          Donald Young
## 510 Multi-Norm_bin_games 2015      Marcos Baghdatis           Lukas Rosol
## 511 Multi-Norm_bin_games 2015      Marcos Baghdatis        Simone Bolelli
## 512 Multi-Norm_bin_games 2015          Rafael Nadal         Stan Wawrinka
## 513 Multi-Norm_bin_games 2015        Jerzy Janowicz           Lukas Rosol
## 514 Multi-Norm_bin_games 2015        Novak Djokovic         Roger Federer
## 515 Multi-Norm_bin_games 2015        Viktor Troicki          Pablo Cuevas
## 516 Multi-Norm_bin_games 2014        Leonardo Mayer   Teymuraz Gabashvili
## 517 Multi-Norm_bin_games 2014          Rafael Nadal        Novak Djokovic
## 518 Multi-Norm_bin_games 2015           Andy Murray         Tomas Berdych
## 519 Multi-Norm_bin_games 2015           Robin Haase     Ricardas Berankis
## 520 Multi-Norm_bin_games 2015        Ernests Gulbis           Lukas Rosol
## 521 Multi-Norm_bin_games 2015          Gilles Simon         Gilles Muller
## 522 Multi-Norm_bin_games 2014        Novak Djokovic          Rafael Nadal
## 523 Multi-Norm_bin_games 2014       Grigor Dimitrov        Vasek Pospisil
## 524 Multi-Norm_bin_games 2014           Andy Murray          David Ferrer
## 525 Multi-Norm_bin_games 2015       Mikhail Youzhny           Blaz Kavcic
## 526 Multi-Norm_bin_games 2015       Nicolas Almagro         Tommy Robredo
## 527 Multi-Norm_bin_games 2015         Tommy Robredo        Simone Bolelli
## 528 Multi-Norm_bin_games 2014         Tomas Berdych       Grigor Dimitrov
## 529 Multi-Norm_bin_games 2014           Andy Murray     Fernando Verdasco
## 530 Multi-Norm_bin_games 2014        Jerzy Janowicz      Adrian Mannarino
## 531 Multi-Norm_bin_games 2015      Santiago Giraldo           Jan Hernych
## 532 Multi-Norm_bin_games 2015           Andy Murray         Kei Nishikori
## 533 Multi-Norm_bin_games 2014       Benjamin Becker           Tatsuma Ito
## 534 Multi-Norm_bin_games 2014       Richard Gasquet        Carlos Berlocq
## 535 Multi-Norm_bin_games 2014       Mikhail Youzhny         Andreas Seppi
## 536 Multi-Norm_bin_games 2014 Philipp Kohlschreiber       Benjamin Becker
## 537 Multi-Norm_bin_games 2015         Bernard Tomic      Adrian Mannarino
## 538 Multi-Norm_bin_games 2015            Ivan Dodig            Joao Sousa
## 539 Multi-Norm_bin_games 2014 Philipp Kohlschreiber     Sergiy Stakhovsky
## 540 Multi-Norm_bin_games 2014        Carlos Berlocq      Julien Benneteau
## 541 Multi-Norm_bin_games 2014        Kevin Anderson         Fabio Fognini
## 542 Multi-Norm_bin_games 2014          Gael Monfils Roberto Bautista Agut
## 543 Multi-Norm_bin_games 2015          David Goffin        Simone Bolelli
## 544 Multi-Norm_bin_games 2015       Richard Gasquet          Ivo Karlovic
## 545 Multi-Norm_bin_games 2014       Dmitry Tursunov           Lukas Rosol
## 546 Multi-Norm_bin_games 2014           Juan Monaco         Jurgen Melzer
## 547 Multi-Norm_bin_games 2014          Gilles Simon           Robin Haase
## 548 Multi-Norm_bin_games 2014        Viktor Troicki        Andrey Golubev
## 549 Multi-Norm_bin_games 2015          David Ferrer            John Isner
## 550 Multi-Norm_bin_games 2015         Tomas Berdych          Gilles Simon
## 551 Multi-Norm_bin_games 2014            Ivan Dodig          Pablo Cuevas
## 552 Multi-Norm_bin_games 2014     Fernando Verdasco        Leonardo Mayer
## 553 Multi-Norm_bin_games 2015       Mikhail Youzhny        Andrey Golubev
## 554 Multi-Norm_bin_games 2015           Lukas Rosol     Sergiy Stakhovsky
## 555 Multi-Norm_bin_games 2015           Marin Cilic        Leonardo Mayer
## 556 Multi-Norm_bin_games 2014         Roger Federer    Jo-Wilfried Tsonga
## 557 Multi-Norm_bin_games 2014        Viktor Troicki           Lukas Rosol
## 558 Multi-Norm_bin_games 2014          Milos Raonic Roberto Bautista Agut
## 559 Multi-Norm_bin_games 2015          Ivo Karlovic      Adrian Mannarino
## 560 Multi-Norm_bin_games 2015         Martin Klizan         Pablo Andujar
## 561 Multi-Norm_bin_games 2015          David Ferrer       Richard Gasquet
## 562 Multi-Norm_bin_games 2015          Rafael Nadal         Bernard Tomic
## 563 Multi-Norm_bin_games 2014           Robin Haase         Denis Istomin
## 564 Multi-Norm_bin_games 2014          Ivo Karlovic       Benjamin Becker
## 565 Multi-Norm_bin_games 2015       Jarkko Nieminen        Andrey Golubev
## 566 Multi-Norm_bin_games 2015       Nicolas Almagro   Alexandr Dolgopolov
## 567 Multi-Norm_bin_games 2014     Nikolay Davydenko          Lukasz Kubot
## 568 Multi-Norm_bin_games 2014          Albert Ramos      Filippo Volandri
## 569 Multi-Norm_bin_games 2014           Sam Querrey     Sergiy Stakhovsky
## 570 Multi-Norm_bin_games 2014           Juan Monaco     Marcel Granollers
## 571 Multi-Norm_bin_games 2014           Juan Monaco        Victor Hanescu
## 572 Multi-Norm_bin_games 2015         Stan Wawrinka        Kevin Anderson
## 573 Multi-Norm_bin_games 2015          Rafael Nadal          Milos Raonic
## 574 Multi-Norm_bin_games 2014       Benjamin Becker          Donald Young
## 575 Multi-Norm_bin_games 2014           Juan Monaco            Joao Sousa
## 576 Multi-Norm_bin_games 2014           Marin Cilic         Tommy Robredo
## 577 Multi-Norm_bin_games 2015          Ivo Karlovic          Dustin Brown
## 578 Multi-Norm_bin_games 2015     Ricardas Berankis          Malek Jaziri
## 579 Multi-Norm_bin_games 2014           Marin Cilic            Ivan Dodig
## 580 Multi-Norm_bin_games 2014         Ryan Harrison            Bjorn Phau
## 581 Multi-Norm_bin_games 2014      Marcos Baghdatis            Rajeev Ram
## 582 Multi-Norm_bin_games 2014          David Ferrer         Tommy Robredo
## 583 Multi-Norm_bin_games 2015        Jerzy Janowicz       Alejandro Falla
## 584 Multi-Norm_bin_games 2015         Fabio Fognini          Aljaz Bedene
## 585 Multi-Norm_bin_games 2015     Sergiy Stakhovsky       Illya Marchenko
## 586 Multi-Norm_bin_games 2015         Tomas Berdych       Grigor Dimitrov
## 587 Multi-Norm_bin_games 2014     Fernando Verdasco        Viktor Troicki
## 588 Multi-Norm_bin_games 2014       Richard Gasquet        Vasek Pospisil
## 589 Multi-Norm_bin_games 2015          Gilles Simon            Joao Sousa
## 590 Multi-Norm_bin_games 2015         Stan Wawrinka          Ivo Karlovic
## 591 Multi-Norm_bin_games 2014        Michael Llodra           Lukas Lacko
## 592 Multi-Norm_bin_games 2014      Julien Benneteau          Pablo Cuevas
## 593 Multi-Norm_bin_games 2014          David Ferrer          David Goffin
## 594 Multi-Norm_bin_games 2015          Dustin Brown         Paolo Lorenzi
## 595 Multi-Norm_bin_games 2015       Thomaz Bellucci         Denis Istomin
## 596 Multi-Norm_bin_games 2015       Feliciano Lopez         Mischa Zverev
## 597 Multi-Norm_bin_games 2014         Tomas Berdych        Ernests Gulbis
## 598 Multi-Norm_bin_games 2014     Fernando Verdasco      Santiago Giraldo
## 599 Multi-Norm_bin_games 2014     Fernando Verdasco     Marcel Granollers
## 600 Multi-Norm_bin_games 2015         Pablo Andujar         Paolo Lorenzi
## 601 Multi-Norm_bin_games 2014           Andy Murray          Gael Monfils
## 602 Multi-Norm_bin_games 2014          Gilles Simon         Gilles Muller
## 603 Multi-Norm_bin_games 2015     Federico Delbonis      Andrey Kuznetsov
## 604 Multi-Norm_bin_games 2014     Nikolay Davydenko        Andrey Golubev
## 605 Multi-Norm_bin_games 2014        Carlos Berlocq   Teymuraz Gabashvili
## 606 Multi-Norm_bin_games 2014           Andy Murray       Grigor Dimitrov
## 607 Multi-Norm_bin_games 2014           Andy Murray          Milos Raonic
## 608 Multi-Norm_bin_games 2015           Sam Querrey       Benjamin Becker
## 609 Multi-Norm_bin_games 2015 Philipp Kohlschreiber       Alejandro Falla
## 610 Multi-Norm_bin_games 2015          David Ferrer       Feliciano Lopez
## 611 Multi-Norm_bin_games 2014          Ivo Karlovic         Matthew Ebden
## 612 Multi-Norm_bin_games 2014          David Ferrer Philipp Kohlschreiber
## 613 Multi-Norm_bin_games 2014         Andreas Seppi       Maximo Gonzalez
## 614 Multi-Norm_bin_games 2014       Richard Gasquet         Gilles Muller
## 615 Multi-Norm_bin_games 2015         Stan Wawrinka          David Goffin
## 616 Multi-Norm_bin_games 2015      Marcos Baghdatis   Teymuraz Gabashvili
## 617 Multi-Norm_bin_games 2015    Jo-Wilfried Tsonga         Bernard Tomic
## 618 Multi-Norm_bin_games 2015 Philipp Kohlschreiber           Robin Haase
## 619 Multi-Norm_bin_games 2015     Fernando Verdasco           Denis Kudla
## 620 Multi-Norm_bin_games 2014 Philipp Kohlschreiber         Denis Istomin
## 621 Multi-Norm_bin_games 2015            Ivan Dodig   Teymuraz Gabashvili
## 622 Multi-Norm_bin_games 2014         Roger Federer         Kei Nishikori
## 623 Multi-Norm_bin_games 2014          Ivo Karlovic           Lukas Rosol
## 624 Multi-Norm_bin_games 2015           Juan Monaco   Teymuraz Gabashvili
## 625 Multi-Norm_bin_games 2015           Marin Cilic         Jeremy Chardy
## 626 Multi-Norm_bin_games 2015       Grigor Dimitrov            Joao Sousa
## 627 Multi-Norm_bin_games 2015         Tomas Berdych             Jack Sock
## 628 Multi-Norm_bin_games 2014   Alexandr Dolgopolov         Fabio Fognini
## 629 Multi-Norm_bin_games 2014        Lleyton Hewitt         Ryan Harrison
## 630 Multi-Norm_bin_games 2014          David Ferrer         Martin Klizan
## 631 Multi-Norm_bin_games 2015          Ivo Karlovic           Lukas Rosol
## 632 Multi-Norm_bin_games 2015        Kevin Anderson          Donald Young
## 633 Multi-Norm_bin_games 2015          Rafael Nadal             Jack Sock
## 634 Multi-Norm_bin_games 2015          Rafael Nadal         Fabio Fognini
## 635 Multi-Norm_bin_games 2015          Rafael Nadal       Grigor Dimitrov
## 636 Multi-Norm_bin_games 2014         Roger Federer         Kei Nishikori
## 637 Multi-Norm_bin_games 2015    Jo-Wilfried Tsonga           Sam Querrey
## 638 Multi-Norm_bin_games 2015      Marcos Baghdatis          Donald Young
## 639 Multi-Norm_bin_games 2015      Santiago Giraldo            Joao Sousa
## 640 Multi-Norm_bin_games 2015    Jo-Wilfried Tsonga         Gilles Muller
## 641 Multi-Norm_bin_games 2015       Richard Gasquet         Gilles Muller
## 642 Multi-Norm_bin_games 2014            Tommy Haas       Benjamin Becker
## 643 Multi-Norm_bin_games 2014       Nicolas Almagro         Jeremy Chardy
## 644 Multi-Norm_bin_games 2014          David Ferrer        Ernests Gulbis
## 645 Multi-Norm_bin_games 2014          Gilles Simon      Filippo Volandri
## 646 Multi-Norm_bin_games 2014        Vasek Pospisil         Paolo Lorenzi
## 647 Multi-Norm_bin_games 2014           Marin Cilic       Feliciano Lopez
## 648 Multi-Norm_bin_games 2014         Roger Federer          Milos Raonic
## 649 Multi-Norm_bin_games 2015        Carlos Berlocq           Guido Pella
## 650 Multi-Norm_bin_games 2015   Alexandr Dolgopolov   Teymuraz Gabashvili
## 651 Multi-Norm_bin_games 2015       Nicolas Almagro        Leonardo Mayer
## 652 Multi-Norm_bin_games 2015      Santiago Giraldo   Rogerio Dutra Silva
## 653 Multi-Norm_bin_games 2015          Rafael Nadal          Ivo Karlovic
## 654 Multi-Norm_bin_games 2015        Kevin Anderson         Fabio Fognini
## 655 Multi-Norm_bin_games 2014           Andy Murray Philipp Kohlschreiber
## 656 Multi-Norm_bin_games 2014         Stan Wawrinka         Tommy Robredo
## 657 Multi-Norm_bin_games 2014         Denis Istomin     Michal Przysiezny
## 658 Multi-Norm_bin_games 2014        Ernests Gulbis   Teymuraz Gabashvili
## 659 Multi-Norm_bin_games 2014           Juan Monaco       Jarkko Nieminen
## 660 Multi-Norm_bin_games 2014           Andy Murray            John Isner
## 661 Multi-Norm_bin_games 2015 Philipp Kohlschreiber      Andrey Kuznetsov
## 662 Multi-Norm_bin_games 2014           Juan Monaco      Horacio Zeballos
## 663 Multi-Norm_bin_games 2014            Tommy Haas       Alejandro Falla
## 664 Multi-Norm_bin_games 2014         Roger Federer          Milos Raonic
## 665 Multi-Norm_bin_games 2014          David Ferrer          Ivo Karlovic
## 666 Multi-Norm_bin_games 2015     Fernando Verdasco   Teymuraz Gabashvili
## 667 Multi-Norm_bin_games 2015        Viktor Troicki         Pablo Andujar
## 668 Multi-Norm_bin_games 2014           Sam Querrey      Santiago Giraldo
## 669 Multi-Norm_bin_games 2014         Tomas Berdych       Feliciano Lopez
## 670 Multi-Norm_bin_games 2015         Tomas Berdych         Fabio Fognini
## 671 Multi-Norm_bin_games 2015         Andreas Seppi   Teymuraz Gabashvili
## 672 Multi-Norm_bin_games 2014        Radek Stepanek       Michael Russell
## 673 Multi-Norm_bin_games 2014 Roberto Bautista Agut      Adrian Mannarino
## 674 Multi-Norm_bin_games 2014         Tommy Robredo         Pablo Andujar
## 675 Multi-Norm_bin_games 2015          David Ferrer          Ivo Karlovic
## 676 Multi-Norm_bin_games 2015          Gilles Simon            Joao Sousa
## 677 Multi-Norm_bin_games 2015           Juan Monaco       Jarkko Nieminen
## 678 Multi-Norm_bin_games 2015           Andy Murray       Richard Gasquet
## 679 Multi-Norm_bin_games 2015           Marin Cilic         Steve Johnson
## 680 Multi-Norm_bin_games 2015          Gael Monfils          Steve Darcis
## 681 Multi-Norm_bin_games 2014          David Ferrer       Grigor Dimitrov
## 682 Multi-Norm_bin_games 2014     Fernando Verdasco          Pablo Cuevas
## 683 Multi-Norm_bin_games 2014          Gael Monfils            Joao Sousa
## 684 Multi-Norm_bin_games 2015     Fernando Verdasco         Paolo Lorenzi
## 685 Multi-Norm_bin_games 2015        Viktor Troicki       Illya Marchenko
## 686 Multi-Norm_bin_games 2015          Rafael Nadal          David Ferrer
## 687 Multi-Norm_bin_games 2015    Jo-Wilfried Tsonga           Lukas Rosol
## 688 Multi-Norm_bin_games 2015        Viktor Troicki            Rajeev Ram
## 689 Multi-Norm_bin_games 2014       Richard Gasquet             Dudi Sela
## 690 Multi-Norm_bin_games 2015         Pablo Andujar      Adrian Mannarino
## 691 Multi-Norm_bin_games 2015       Richard Gasquet        Simone Bolelli
## 692 Multi-Norm_bin_games 2015         Tommy Robredo         Pablo Andujar
## 693 Multi-Norm_bin_games 2015           Marin Cilic          Donald Young
## 694 Multi-Norm_bin_games 2014          David Ferrer         Jeremy Chardy
## 695 Multi-Norm_bin_games 2014          David Ferrer         Fabio Fognini
## 696 Multi-Norm_bin_games 2014          David Ferrer        Ernests Gulbis
## 697 Multi-Norm_bin_games 2014        Kevin Anderson       Stephane Robert
## 698 Multi-Norm_bin_games 2014           Juan Monaco        Andrey Golubev
## 699 Multi-Norm_bin_games 2014          David Ferrer            Ivan Dodig
## 700 Multi-Norm_bin_games 2014         Roger Federer          Gael Monfils
## 701 Multi-Norm_bin_games 2014          David Ferrer      Julien Benneteau
## 702 Multi-Norm_bin_games 2015          Gael Monfils        Simone Bolelli
## 703 Multi-Norm_bin_games 2015          David Ferrer         Bernard Tomic
## 704 Multi-Norm_bin_games 2015     Fernando Verdasco   Teymuraz Gabashvili
## 705 Multi-Norm_bin_games 2015        Ernests Gulbis         Igor Sijsling
## 706 Multi-Norm_bin_games 2015        Ernests Gulbis          Marsel Ilhan
## 707 Multi-Norm_bin_games 2015 Roberto Bautista Agut   Teymuraz Gabashvili
## 708 Multi-Norm_bin_games 2015         Tomas Berdych             Jack Sock
## 709 Multi-Norm_bin_games 2015         Roger Federer          Gael Monfils
## 710 Multi-Norm_bin_games 2014 Philipp Kohlschreiber        Simone Bolelli
## 711 Multi-Norm_bin_games 2014       Richard Gasquet         Martin Klizan
## 712 Multi-Norm_bin_games 2014         Roger Federer          Milos Raonic
## 713 Multi-Norm_bin_games 2015          Ivo Karlovic           Tatsuma Ito
## 714 Multi-Norm_bin_games 2015     Federico Delbonis   Rogerio Dutra Silva
## 715 Multi-Norm_bin_games 2014     Fernando Verdasco          Donald Young
## 716 Multi-Norm_bin_games 2014           Andy Murray     Marcel Granollers
## 717 Multi-Norm_bin_games 2014           Andy Murray      Julien Benneteau
## 718 Multi-Norm_bin_games 2015         Tomas Berdych         Bernard Tomic
## 719 Multi-Norm_bin_games 2015          Gael Monfils           Lukas Rosol
## 720 Multi-Norm_bin_games 2014 Philipp Kohlschreiber         Denis Istomin
## 721 Multi-Norm_bin_games 2014           Marin Cilic     Mikhail Kukushkin
## 722 Multi-Norm_bin_games 2015       Richard Gasquet          Ivo Karlovic
## 723 Multi-Norm_bin_games 2015          David Ferrer           Marin Cilic
## 724 Multi-Norm_bin_games 2015    Jo-Wilfried Tsonga          Benoit Paire
## 725 Multi-Norm_bin_games 2014          Gilles Simon          Donald Young
## 726 Multi-Norm_bin_games 2014            Tommy Haas      Horacio Zeballos
## 727 Multi-Norm_bin_games 2014     Nikolay Davydenko             Dudi Sela
## 728 Multi-Norm_bin_games 2014         Roger Federer         Stan Wawrinka
## 729 Multi-Norm_bin_games 2015     Fernando Verdasco       Maximo Gonzalez
## 730 Multi-Norm_bin_games 2015          Rafael Nadal         Tomas Berdych
## 731 Multi-Norm_bin_games 2014         Roger Federer   Alexandr Dolgopolov
## 732 Multi-Norm_bin_games 2015          Rafael Nadal        Kevin Anderson
## 733 Multi-Norm_bin_games 2015          Rafael Nadal        Kevin Anderson
## 734 Multi-Norm_bin_games 2015        Carlos Berlocq       Illya Marchenko
## 735 Multi-Norm_bin_games 2015         Roger Federer         Stan Wawrinka
## 736 Multi-Norm_bin_games 2014            Tommy Haas         Wayne Odesnik
## 737 Multi-Norm_bin_games 2014           Juan Monaco       Benjamin Becker
## 738 Multi-Norm_bin_games 2014     Fernando Verdasco        Michael Llodra
## 739 Multi-Norm_bin_games 2014         Stan Wawrinka     Marinko Matosevic
## 740 Multi-Norm_bin_games 2014           Andy Murray         Tommy Robredo
## 741 Multi-Norm_bin_games 2014           Juan Monaco         Paolo Lorenzi
## 742 Multi-Norm_bin_games 2015       Richard Gasquet        Simone Bolelli
## 743 Multi-Norm_bin_games 2015 Philipp Kohlschreiber           Lukas Rosol
## 744 Multi-Norm_bin_games 2015          David Ferrer     Mikhail Kukushkin
## 745 Multi-Norm_bin_games 2014          David Ferrer            John Isner
## 746 Multi-Norm_bin_games 2014        Novak Djokovic       Grigor Dimitrov
## 747 Multi-Norm_bin_games 2015         Roger Federer       Grigor Dimitrov
## 748 Multi-Norm_bin_games 2015           Andy Murray       Grigor Dimitrov
## 749 Multi-Norm_bin_games 2015         Roger Federer          Pablo Cuevas
## 750 Multi-Norm_bin_games 2014       Mikhail Youzhny       Benjamin Becker
## 751 Multi-Norm_bin_games 2014           Juan Monaco             Pere Riba
## 752 Multi-Norm_bin_games 2015          Rafael Nadal         Jeremy Chardy
## 753 Multi-Norm_bin_games 2015        Novak Djokovic         Stan Wawrinka
## 754 Multi-Norm_bin_games 2014     Fernando Verdasco      Horacio Zeballos
## 755 Multi-Norm_bin_games 2014       Richard Gasquet         Bernard Tomic
## 756 Multi-Norm_bin_games 2014         Roger Federer          Gael Monfils
## 757 Multi-Norm_bin_games 2014          Rafael Nadal        Simone Bolelli
## 758 Multi-Norm_bin_games 2015        Novak Djokovic         Stan Wawrinka
## 759 Multi-Norm_bin_games 2015          David Ferrer         Fabio Fognini
## 760 Multi-Norm_bin_games 2015          Rafael Nadal        Vasek Pospisil
## 761 Multi-Norm_bin_games 2014          Rafael Nadal       Grigor Dimitrov
## 762 Multi-Norm_bin_games 2014         Andreas Seppi      Adrian Mannarino
## 763 Multi-Norm_bin_games 2014           Andy Murray         Tommy Robredo
## 764 Multi-Norm_bin_games 2015           Marin Cilic      Andrey Kuznetsov
## 765 Multi-Norm_bin_games 2015          David Ferrer         Fabio Fognini
## 766 Multi-Norm_bin_games 2014       Mikhail Youzhny     Michal Przysiezny
## 767 Multi-Norm_bin_games 2014         Roger Federer          Gilles Simon
## 768 Multi-Norm_bin_games 2014         Roger Federer       Grigor Dimitrov
## 769 Multi-Norm_bin_games 2015       Richard Gasquet         Pablo Andujar
## 770 Multi-Norm_bin_games 2015           Marin Cilic         Mischa Zverev
## 771 Multi-Norm_bin_games 2015           Marin Cilic            Joao Sousa
## 772 Multi-Norm_bin_games 2014         Tomas Berdych         Martin Klizan
## 773 Multi-Norm_bin_games 2015      Santiago Giraldo   Rogerio Dutra Silva
## 774 Multi-Norm_bin_games 2014            John Isner         Pablo Andujar
## 775 Multi-Norm_bin_games 2014        Novak Djokovic         Kei Nishikori
## 776 Multi-Norm_bin_games 2014        Novak Djokovic       Grigor Dimitrov
## 777 Multi-Norm_bin_games 2014         Roger Federer          David Goffin
## 778 Multi-Norm_bin_games 2014        Novak Djokovic            John Isner
## 779 Multi-Norm_bin_games 2014          David Ferrer         Pablo Andujar
## 780 Multi-Norm_bin_games 2014         Roger Federer       Feliciano Lopez
## 781 Multi-Norm_bin_games 2015     Fernando Verdasco              Go Soeda
## 782 Multi-Norm_bin_games 2015          Milos Raonic            Joao Sousa
## 783 Multi-Norm_bin_games 2015          Rafael Nadal       Grigor Dimitrov
## 784 Multi-Norm_bin_games 2014           Andy Murray       Feliciano Lopez
## 785 Multi-Norm_bin_games 2014         Roger Federer      Julien Benneteau
## 786 Multi-Norm_bin_games 2014           Andy Murray        Vasek Pospisil
## 787 Multi-Norm_bin_games 2015          Rafael Nadal         Fabio Fognini
## 788 Multi-Norm_bin_games 2014          Rafael Nadal   Alexandr Dolgopolov
## 789 Multi-Norm_bin_games 2014          Rafael Nadal           Andy Murray
## 790 Multi-Norm_bin_games 2014    Jo-Wilfried Tsonga            Jimmy Wang
## 791 Multi-Norm_bin_games 2014         Roger Federer Roberto Bautista Agut
## 792 Multi-Norm_bin_games 2014         Tomas Berdych      Adrian Mannarino
## 793 Multi-Norm_bin_games 2015          Rafael Nadal           Lukas Rosol
## 794 Multi-Norm_bin_games 2015        Novak Djokovic            John Isner
## 795 Multi-Norm_bin_games 2015          Rafael Nadal          Pablo Cuevas
## 796 Multi-Norm_bin_games 2015         Stan Wawrinka            Joao Sousa
## 797 Multi-Norm_bin_games 2015          Rafael Nadal            John Isner
## 798 Multi-Norm_bin_games 2015          Rafael Nadal     Fernando Verdasco
## 799 Multi-Norm_bin_games 2015          Rafael Nadal           Lukas Rosol
## 800 Multi-Norm_bin_games 2014           Andy Murray       Feliciano Lopez
## 801 Multi-Norm_bin_games 2014        Novak Djokovic        Ernests Gulbis
## 802 Multi-Norm_bin_games 2014         Roger Federer        Vasek Pospisil
## 803 Multi-Norm_bin_games 2015          Rafael Nadal          Donald Young
## 804 Multi-Norm_bin_games 2015          Rafael Nadal            John Isner
## 805 Multi-Norm_bin_games 2014         Tomas Berdych   Teymuraz Gabashvili
## 806 Multi-Norm_bin_games 2014           Andy Murray         Fabio Fognini
## 807 Multi-Norm_bin_games 2015          Rafael Nadal           Juan Monaco
## 808 Multi-Norm_bin_games 2014           Andy Murray         Pablo Andujar
## 809 Multi-Norm_bin_games 2015          Rafael Nadal             Dudi Sela
## 810 Multi-Norm_bin_games 2014         Roger Federer           Lukas Rosol
## 811 Multi-Norm_bin_games 2015          Rafael Nadal        Carlos Berlocq
## 812 Multi-Norm_bin_games 2015          Rafael Nadal         Andreas Seppi
## 813 Multi-Norm_bin_games 2014           Andy Murray    Matthias Bachinger
##                    score2  MaxW  MaxL  AvgW AvgL best_winner_exp_payout
## 1         6-7 7-6 7-5 7-6 61.00  1.01 22.96 1.01             2.66498649
## 2             7-6 7-6 6-4 46.00  1.02 20.68 1.01             3.46513678
## 3         7-6 6-1 3-6 7-6 39.75  1.02 20.78 1.01             2.54670227
## 4             6-4 7-5 7-6 10.50  1.10  7.81 1.08             1.28018460
## 5             6-3 3-6 6-3 10.50  1.08  8.42 1.06             1.09636746
## 6             7-6 6-3 7-6 10.15  1.14  7.57 1.08             0.31892071
## 7     2-6 6-4 6-2 3-6 9-7  9.95  1.12  7.54 1.09             0.10184309
## 8     6-4 3-6 4-6 7-6 6-4  9.87  1.09  8.23 1.07             1.21386336
## 9                 6-3 7-5  9.50  1.11  7.98 1.07             2.08864975
## 10                7-6 6-2  9.00  1.12  7.30 1.09             0.70329361
## 11                7-6 6-4  8.78  1.11  7.33 1.09             0.92774694
## 12        6-3 6-4 5-7 6-2  8.50  1.15  6.65 1.11             3.31034619
## 13        7-6 6-4 6-7 6-3  8.45  1.12  7.10 1.09             0.72128876
## 14                6-3 7-5  7.50  1.15  6.32 1.11             1.48486578
## 15    4-6 6-4 6-3 2-6 7-5  7.50  1.18  5.68 1.13             0.17009961
## 16                6-4 6-2  7.14  1.15  5.98 1.12             0.45975165
## 17            6-4 2-6 6-3  7.09  1.15  5.70 1.13             0.57839195
## 18                6-3 6-3  7.00  1.15  6.07 1.12             0.07125206
## 19                6-2 6-2  6.92  1.17  5.69 1.14             0.32620001
## 20            7-5 4-6 6-0  6.80  1.17  5.78 1.12             0.91377741
## 21            7-6 6-1 6-2  6.75  1.19  5.60 1.14             0.74101237
## 22                6-4 6-4  6.65  1.17  5.58 1.14             0.07726900
## 23            6-3 4-6 6-3  6.50  1.15  5.78 1.13             0.59925446
## 24            5-7 7-6 6-3  6.49  1.20  5.14 1.15             0.29700838
## 25            6-7 6-3 7-6  6.25  1.18  5.37 1.14             0.07268252
## 26            6-4 6-2 6-2  6.10  1.21  5.02 1.17             0.92326193
## 27            6-1 6-2 6-2  5.97  1.22  5.05 1.17             1.51876606
## 28        6-3 6-2 3-6 6-3  5.96  1.25  5.19 1.17             0.19271866
## 29            5-7 7-6 6-4  5.81  1.19  5.15 1.16             0.51435280
## 30                6-4 6-4  5.81  1.17  5.13 1.15             1.04106713
## 31                6-2 7-6  5.76  1.20  5.07 1.16             0.63416942
## 32                6-2 6-2  5.75  1.20  5.08 1.16             2.78734280
## 33            6-4 6-7 6-3  5.68  1.20  4.90 1.17             0.88154659
## 34            7-6 6-7 6-4  5.63  1.20  4.88 1.17             0.49636711
## 35                6-4 7-6  5.60  1.22  4.73 1.18             0.89785786
## 36            5-7 6-2 6-3  5.54  1.22  4.80 1.17             1.29036138
## 37            6-4 3-6 7-6  5.50  1.20  4.72 1.17             0.09978649
## 38    6-3 7-6 2-6 4-6 6-4  5.50  1.22  4.94 1.17             0.54030507
## 39                6-3 6-2  5.33  1.25  4.36 1.20             1.39886688
## 40        6-7 6-4 6-2 6-0  5.30  1.25  4.32 1.21             0.17792203
## 41            7-6 4-6 6-1  5.25  1.26  4.52 1.19             0.85207463
## 42                6-4 7-5  5.23  1.22  4.38 1.20             0.64647710
## 43            1-6 6-4 6-2  5.05  1.23  4.46 1.20             0.36519285
## 44            0-6 7-5 6-1  5.00  1.25  4.54 1.19             0.33386514
## 45            2-6 6-1 6-2  5.00  1.25  4.31 1.21             0.72167451
## 46                6-4 7-6  5.00  1.25  4.19 1.22             0.26635214
## 47            6-3 6-7 6-4  5.00  1.22  4.38 1.20             0.23651109
## 48                7-5 6-3  4.95  1.26  4.12 1.22             0.20866541
## 49            6-4 6-7 7-6  4.77  1.29  3.92 1.24             0.62807925
## 50            6-2 6-7 6-3  4.77  1.30  4.03 1.23             0.42112861
## 51                6-4 6-4  4.75  1.26  4.13 1.22             0.15225871
## 52            3-6 6-2 6-1  4.70  1.28  4.24 1.21             0.61720857
## 53            7-5 7-6 7-5  4.65  1.25  4.31 1.21             0.67762137
## 54                6-4 7-6  4.65  1.26  4.15 1.22             0.23516051
## 55                6-2 6-3  4.63  1.27  4.13 1.22             0.88007783
## 56            3-6 6-3 6-2  4.60  1.27  4.17 1.22             0.91341935
## 57        6-3 3-6 6-1 6-3  4.60  1.27  4.24 1.22             0.24575193
## 58            7-5 2-6 7-6  4.57  1.26  4.14 1.22             0.36869718
## 59                6-3 7-6  4.55  1.27  3.97 1.24             0.20599750
## 60            4-6 6-3 6-4  4.50  1.27  4.19 1.22             0.24379054
## 61                6-4 6-4  4.50  1.29  3.93 1.23             0.35795470
## 62                6-2 6-2  4.48  1.29  3.96 1.24             0.19753799
## 63                6-4 6-2  4.45  1.29  3.89 1.25             0.18714370
## 64            6-4 3-6 6-3  4.44  1.27  3.94 1.24             0.94843778
## 65                6-4 6-4  4.38  1.29  3.95 1.24             0.22335822
## 66            6-4 7-6 7-6  4.36  1.30  3.97 1.26             2.50941193
## 67                6-1 6-4  4.34  1.26  3.93 1.24             1.13689131
## 68    7-6 6-3 5-7 5-7 7-5  4.33  1.29  3.98 1.24             0.54992912
## 69            3-6 6-3 7-6  4.33  1.29  3.94 1.24             0.16792624
## 70    4-6 7-6 6-7 6-1 6-2  4.30  1.33  3.77 1.26             0.58214532
## 71    1-6 3-6 6-3 6-0 6-2  4.30  1.30  3.71 1.27             0.57291296
## 72            6-4 6-7 6-3  4.30  1.30  3.79 1.26             0.41155777
## 73                6-4 6-2  4.30  1.29  3.78 1.26             0.28334651
## 74                7-6 6-4  4.30  1.29  3.86 1.25             0.52138337
## 75            3-6 7-5 6-3  4.30  1.30  3.81 1.25             0.17429960
## 76            6-1 6-3 7-5  4.30  1.29  3.80 1.26             0.74180619
## 77                6-3 6-4  4.26  1.29  3.83 1.25             0.07567580
## 78    2-6 6-4 6-2 3-6 6-3  4.25  1.28  3.90 1.24             0.22140584
## 79                6-1 6-4  4.23  1.30  3.83 1.25             0.65535604
## 80                7-6 6-3  4.22  1.29  3.76 1.26             0.18482219
## 81                6-4 7-6  4.22  1.29  3.81 1.25             0.09205364
## 82            5-7 6-1 6-4  4.20  1.33  3.61 1.28             0.37082406
## 83                6-2 7-6  4.20  1.30  3.70 1.26             0.39617936
## 84                6-4 6-4  4.20  1.29  3.78 1.25             0.31921768
## 85            6-7 6-4 6-4  4.15  1.30  3.78 1.26             0.12247368
## 86                6-4 7-5  4.15  1.30  3.82 1.25             0.30798281
## 87            6-4 4-6 6-4  4.13  1.29  3.79 1.25             0.74599993
## 88                7-6 6-4  4.06  1.30  3.58 1.28             0.17296766
## 89                7-5 6-3  4.01  1.31  3.65 1.27             0.68624267
## 90                6-3 7-5  4.00  1.33  3.67 1.27             0.95308052
## 91            2-6 6-1 6-2  4.00  1.35  3.61 1.28             0.74725224
## 92                7-5 7-6  4.00  1.33  3.54 1.29             0.32927403
## 93                7-5 6-2  4.00  1.34  3.60 1.29             0.61591664
## 94                6-2 7-6  4.00  1.33  3.54 1.28             0.20607633
## 95            6-4 4-6 6-3  4.00  1.49  2.78 1.44             0.38626173
## 96            4-6 6-3 6-4  4.00  1.34  3.70 1.27             0.58590878
## 97                6-2 6-4  3.97  1.35  3.50 1.29             0.41637383
## 98                7-5 6-4  3.95  1.35  3.43 1.30             0.60303774
## 99            7-5 6-7 6-3  3.92  1.35  3.41 1.31             0.30427455
## 100               7-6 6-4  3.90  1.36  3.27 1.32             0.36729570
## 101   6-1 6-4 4-6 3-6 6-3  3.90  1.45  3.55 1.30             0.79674664
## 102           1-6 6-1 6-2  3.85  1.32  3.53 1.29             0.18043386
## 103               6-2 7-6  3.85  1.35  3.36 1.31             0.31511532
## 104           7-6 4-6 6-0  3.83  1.33  3.47 1.30             0.24218378
## 105               6-1 7-6  3.80  1.31  3.54 1.28             0.66384448
## 106   4-6 6-7 6-4 6-3 6-3  3.77  1.36  3.40 1.32             0.79134048
## 107               7-5 6-2  3.75  1.37  3.35 1.32             0.40422396
## 108           3-6 6-3 7-6  3.75  1.36  3.38 1.31             0.28136703
## 109               6-1 6-1  3.71  1.37  3.32 1.32             0.17705924
## 110               6-2 6-0  3.70  1.38  3.25 1.33             0.12977807
## 111           4-6 6-3 7-5  3.70  1.38  3.36 1.31             0.58453551
## 112           7-6 6-7 6-3  3.65  1.39  3.27 1.32             0.53442820
## 113               7-6 7-6  3.65  1.36  3.31 1.32             0.65161816
## 114           6-3 3-6 6-1  3.65  1.37  3.16 1.34             0.14381982
## 115               6-4 6-4  3.64  1.39  3.16 1.34             0.48742657
## 116   6-3 2-6 4-6 7-6 6-4  3.60  1.40  3.36 1.31             0.29540934
## 117           7-5 2-6 7-5  3.60  1.40  3.15 1.35             0.18039041
## 118               7-6 6-3  3.60  1.36  3.38 1.31             0.66248046
## 119               6-4 6-4  3.60  1.40  3.24 1.34             0.47448032
## 120           5-7 6-1 7-5  3.60  1.35  3.32 1.32             0.35946296
## 121           6-4 4-6 7-5  3.59  1.38  3.17 1.34             0.68868892
## 122           6-4 6-3 7-6  3.56  1.38  3.35 1.32             0.71638137
## 123               7-6 6-4  3.56  1.36  3.31 1.32             0.14911266
## 124               6-3 7-5  3.55  1.38  3.28 1.32             1.02006199
## 125           7-6 3-6 7-6  3.50  1.43  3.12 1.35             0.51310759
## 126               6-3 6-3  3.50  1.40  3.17 1.34             0.17592132
## 127               6-4 6-3  3.50  1.40  3.13 1.36             0.52290134
## 128               7-6 6-4  3.50  1.37  3.23 1.33             0.31834499
## 129           1-6 6-1 6-4  3.50  1.39  3.15 1.35             0.42232035
## 130               7-5 6-3  3.50  1.40  3.17 1.34             0.09646319
## 131           7-6 6-3 7-6  3.50  1.54  2.63 1.48             1.78863657
## 132               6-4 7-6  3.50  1.38  3.22 1.33             0.22912827
## 133               6-1 6-2  3.50  1.36  3.28 1.32             0.74363895
## 134           6-4 0-6 7-5  3.50  1.42  3.10 1.37             0.09222030
## 135               6-3 6-4  3.45  1.38  3.14 1.35             0.17011879
## 136               7-6 7-6  3.45  1.41  3.16 1.34             0.35626594
## 137           7-6 4-6 6-3  3.43  1.40  3.14 1.34             0.53359452
## 138               7-6 6-1  3.40  1.43  2.99 1.38             0.63002832
## 139           6-4 3-6 6-1  3.40  1.40  3.20 1.34             0.11156114
## 140               7-6 7-6  3.40  1.42  3.10 1.35             0.79167283
## 141           6-1 6-2 6-4  3.40  1.41  3.15 1.35             0.37341098
## 142           5-7 7-6 6-4  3.40  1.41  3.07 1.36             0.20383065
## 143           7-6 4-6 6-4  3.39  1.42  3.03 1.37             0.19351024
## 144               6-3 7-6  3.35  1.40  3.15 1.34             1.26998896
## 145           6-3 6-7 6-4  3.35  1.42  3.08 1.36             0.07340687
## 146               6-2 6-3  3.33  1.40  3.10 1.35             0.67187642
## 147           3-6 7-6 7-6  3.30  1.39  3.11 1.35             0.62131168
## 148           6-3 4-6 6-3  3.30  1.40  3.05 1.36             0.41107924
## 149           7-6 3-6 6-0  3.30  1.44  3.00 1.37             0.36074776
## 150               7-6 7-5  3.30  1.41  3.06 1.36             0.16752454
## 151               7-6 7-5  3.30  1.40  3.03 1.36             0.24749587
## 152           6-4 1-6 7-5  3.30  1.41  3.09 1.36             0.48787424
## 153       6-7 6-2 7-6 7-5  3.28  1.44  2.94 1.39             0.30983173
## 154               7-5 6-4  3.28  1.48  2.85 1.41             0.11217430
## 155           6-2 4-6 6-4  3.28  1.45  2.93 1.38             0.08700593
## 156               6-4 6-3  3.28  1.45  2.92 1.39             0.31436987
## 157       6-7 7-5 6-3 6-2  3.25  1.45  2.83 1.42             1.41307798
## 158           3-6 7-6 6-4  3.25  1.44  3.01 1.37             0.08802130
## 159           3-6 6-1 6-4  3.25  1.43  2.99 1.38             0.41770834
## 160       6-3 1-6 7-6 6-3  3.25  1.48  3.01 1.38             0.09792971
## 161               7-6 6-3  3.25  1.44  3.04 1.37             0.15194073
## 162           7-6 2-6 7-6  3.23  1.46  2.84 1.40             0.10338734
## 163           7-5 3-6 7-6  3.20  1.44  2.96 1.38             0.49334023
## 164               7-6 6-3  3.20  1.50  2.79 1.42             0.42457393
## 165               6-4 6-4  3.20  1.43  2.91 1.39             0.26385638
## 166   6-1 7-6 3-6 3-6 6-4  3.20  1.48  2.98 1.38             0.10646216
## 167       6-3 6-2 6-7 6-3  3.20  1.44  2.96 1.39             0.43358903
## 168               6-3 6-2  3.15  1.43  2.92 1.39             0.07514904
## 169               6-3 7-5  3.14  1.52  2.75 1.45             0.25276046
## 170               6-4 6-3  3.13  1.48  2.79 1.42             0.13034217
## 171               7-6 6-4  3.12  1.44  2.87 1.40             0.06348964
## 172       6-1 6-4 4-6 6-0  3.12  1.42  2.99 1.38             1.01541283
## 173           7-6 6-7 6-2  3.10  1.51  2.73 1.43             0.37137148
## 174       6-4 7-6 6-7 6-4  3.10  1.51  2.80 1.42             0.28201798
## 175               7-5 6-4  3.10  1.45  2.88 1.40             0.49283101
## 176       5-7 6-3 6-4 6-1  3.10  1.44  2.94 1.39             0.92172986
## 177               7-6 7-6  3.10  1.44  2.97 1.38             0.25067554
## 178               7-5 6-4  3.09  1.47  2.86 1.40             0.43689667
## 179 6-7 6-4 3-6 6-3 16-14  3.05  1.50  2.83 1.42             1.37211508
## 180               7-6 7-5  3.05  1.47  2.76 1.42             0.55107769
## 181               7-6 6-3  3.05  1.50  2.70 1.44             0.84147837
## 182               6-4 6-4  3.01  1.73  2.33 1.59             0.13202026
## 183               6-4 7-6  3.00  1.50  2.79 1.42             0.08066648
## 184               7-6 6-3  3.00  1.51  2.72 1.44             0.44596818
## 185           6-3 6-4 6-1  3.00  1.52  2.76 1.43             0.30283826
## 186               6-0 6-3  3.00  1.53  2.74 1.43             0.31523069
## 187               7-6 6-4  3.00  1.48  2.80 1.41             0.08044052
## 188               6-2 6-4  3.00  1.49  2.75 1.43             0.27665431
## 189               6-3 7-6  3.00  1.49  2.77 1.42             0.47565760
## 190               7-6 7-6  3.00  1.55  2.69 1.46             0.24193622
## 191       2-6 6-3 6-4 7-6  3.00  1.48  2.85 1.41             0.19895975
## 192           6-3 7-5 6-1  3.00  1.45  2.84 1.41             0.94276761
## 193           7-6 2-6 6-2  3.00  1.50  2.75 1.43             0.60517135
## 194               7-6 7-6  2.97  1.45  2.80 1.42             0.15225772
## 195               7-6 6-3  2.95  1.50  2.71 1.45             0.34352813
## 196               6-1 6-2  2.95  1.50  2.74 1.43             0.33467083
## 197           7-5 6-4 6-4  2.95  1.57  2.65 1.47             0.33226190
## 198               6-4 6-2  2.95  1.55  2.73 1.43             0.76987067
## 199               7-6 6-3  2.95  1.52  2.72 1.43             0.44149278
## 200               6-1 7-6  2.90  1.60  2.64 1.47             0.43060076
## 201           6-4 2-6 6-2  2.90  1.55  2.57 1.49             0.35107278
## 202           2-6 7-6 6-4  2.90  1.48  2.75 1.43             0.31844789
## 203               6-3 7-6  2.90  1.60  2.57 1.49             0.26833773
## 204           7-5 4-6 6-1  2.90  1.50  2.66 1.46             0.73582904
## 205       7-6 6-1 6-7 6-1  2.88  1.55  2.56 1.49             0.14714542
## 206           6-2 6-3 6-4  2.88  1.53  2.63 1.47             0.59997124
## 207               6-4 7-5  2.88  1.53  2.66 1.46             0.46674314
## 208               7-6 7-5  2.87  1.50  2.69 1.45             0.84556749
## 209           6-3 3-6 6-4  2.86  1.55  2.59 1.48             0.55851703
## 210               7-6 6-3  2.85  1.55  2.61 1.48             0.39964319
## 211               6-3 7-5  2.85  1.55  2.68 1.46             0.81070542
## 212               6-4 6-2  2.85  1.59  2.68 1.45             0.38002250
## 213           6-1 5-7 6-4  2.80  1.60  2.52 1.51             0.46656843
## 214               7-6 6-2  2.80  1.54  2.58 1.49             0.51847078
## 215           6-4 5-7 6-4  2.80  1.54  2.60 1.48             0.11183105
## 216               6-3 6-1  2.80  1.54  2.57 1.49             0.62121428
## 217               6-4 7-6  2.80  1.53  2.55 1.49             0.41520003
## 218       7-5 3-6 6-2 6-1  2.80  1.57  2.59 1.49             0.33986328
## 219           7-6 6-7 6-3  2.80  1.58  2.52 1.50             0.33027185
## 220       6-4 4-6 6-3 6-3  2.80  1.52  2.62 1.48             0.19895035
## 221  6-4 4-6 3-6 6-4 11-9  2.80  1.55  2.68 1.47             0.41173538
## 222               7-6 7-6  2.80  1.50  2.68 1.45             0.30821567
## 223           6-4 1-6 6-4  2.80  1.50  2.67 1.46             0.69208833
## 224           6-2 6-7 6-2  2.78  1.54  2.58 1.48             0.29353399
## 225           6-3 7-5 6-3  2.78  1.59  2.54 1.51             0.45370627
## 226               6-2 7-5  2.77  1.55  2.58 1.48             0.07723036
## 227           6-3 2-6 6-2  2.75  1.63  2.46 1.53             0.21754851
## 228           4-6 6-1 7-5  2.75  1.57  2.50 1.51             0.20238665
## 229               6-2 6-1  2.75  1.63  2.55 1.49             0.23531779
## 230       7-6 7-6 6-7 7-5  2.75  1.62  2.52 1.52             0.06138149
## 231               6-4 6-4  2.75  1.63  2.51 1.52             0.29477992
## 232               6-4 6-1  2.75  1.61  2.52 1.51             0.59856948
## 233           6-7 7-6 7-6  2.75  1.57  2.58 1.49             0.45792471
## 234           3-6 7-6 6-4  2.75  1.58  2.59 1.47             0.25032302
## 235           5-7 6-3 7-5  2.75  1.76  2.21 1.63             0.34897566
## 236           4-6 6-0 6-3  2.75  1.54  2.57 1.48             0.12476866
## 237           6-3 6-7 6-4  2.72  1.56  2.50 1.52             0.13556435
## 238               6-3 7-6  2.71  1.60  2.47 1.53             0.26435115
## 239           6-7 6-1 6-4  2.71  1.57  2.52 1.50             0.60842372
## 240               7-6 7-6  2.70  1.67  2.31 1.59             0.14864325
## 241               6-4 6-1  2.70  1.60  2.50 1.54             0.32357090
## 242               6-3 6-2  2.70  1.61  2.41 1.54             0.08795623
## 243               7-6 6-3  2.70  1.57  2.54 1.50             0.56684307
## 244           2-6 6-2 7-5  2.70  1.62  2.51 1.50             0.57687037
## 245               6-2 6-4  2.70  1.65  2.32 1.58             0.59686033
## 246               6-4 6-2  2.70  1.55  2.54 1.50             0.33834636
## 247               6-4 6-1  2.70  1.57  2.46 1.52             0.11639562
## 248               7-6 7-6  2.70  1.63  2.55 1.50             0.31989736
## 249               6-3 6-2  2.66  1.56  2.55 1.50             0.08192542
## 250               6-4 6-4  2.66  1.67  2.28 1.61             0.12402599
## 251               6-1 6-1  2.65  1.67  2.40 1.56             0.33171470
## 252           7-6 3-6 6-3  2.65  1.61  2.47 1.53             0.11442195
## 253               6-3 6-3  2.65  1.67  2.44 1.54             0.15938489
## 254           7-6 6-7 7-6  2.65  1.57  2.47 1.53             0.10044155
## 255               7-5 6-3  2.65  1.62  2.39 1.56             0.10444331
## 256               6-1 6-3  2.65  1.63  2.39 1.55             0.22412817
## 257               6-4 7-6  2.65  1.60  2.44 1.54             0.12857883
## 258               7-6 6-3  2.64  1.61  2.51 1.51             0.11115758
## 259               6-4 6-4  2.63  1.64  2.45 1.53             0.17790078
## 260               6-4 6-2  2.63  1.59  2.42 1.54             0.71229543
## 261           6-4 1-6 7-6  2.63  1.58  2.48 1.52             0.13548920
## 262               6-1 7-6  2.61  1.67  2.25 1.63             0.24896358
## 263               6-2 6-4  2.60  1.69  2.32 1.59             0.23437006
## 264       7-6 4-6 7-6 7-6  2.60  1.66  2.38 1.57             0.29225566
## 265               6-4 6-3  2.60  1.62  2.38 1.56             0.69921915
## 266           3-6 6-3 6-1  2.56  1.68  2.40 1.55             0.47700548
## 267               7-6 6-4  2.56  1.62  2.40 1.55             0.11699436
## 268               7-5 6-4  2.55  1.63  2.38 1.56             0.08432603
## 269               6-2 6-2  2.55  1.69  2.27 1.62             0.14239998
## 270           7-6 6-4 7-6  2.55  1.68  2.33 1.60             0.25324149
## 271           6-7 7-6 7-6  2.55  1.63  2.35 1.57             0.07784658
## 272           6-3 6-4 6-2  2.55  1.63  2.46 1.54             0.20235503
## 273               6-3 7-6  2.55  1.62  2.39 1.56             0.19589041
## 274               6-3 6-2  2.55  1.71  2.30 1.61             0.42655246
## 275               7-6 6-1  2.52  1.67  2.36 1.57             0.10902496
## 276               6-3 7-6  2.50  1.68  2.33 1.58             0.37033899
## 277           6-1 3-6 6-1  2.50  1.67  2.32 1.59             0.57565924
## 278           4-6 6-3 6-4  2.50  1.71  2.31 1.59             0.30204618
## 279               6-3 6-4  2.50  1.67  2.33 1.58             0.19460527
## 280           7-5 2-6 6-3  2.50  1.72  2.35 1.58             0.52568487
## 281           3-6 7-6 7-6  2.50  1.68  2.35 1.56             0.39955039
## 282               6-4 7-6  2.50  1.65  2.34 1.57             0.16550146
## 283               7-6 6-4  2.50  1.71  2.30 1.60             0.37530160
## 284               6-2 7-6  2.50  1.63  2.32 1.58             0.15525445
## 285           6-4 1-6 6-4  2.47  1.67  2.27 1.60             0.14466833
## 286               6-4 7-6  2.45  1.66  2.33 1.59             0.17635749
## 287               6-3 6-2  2.45  1.65  2.30 1.60             0.70137403
## 288               6-2 6-4  2.45  1.73  2.17 1.67             0.13647509
## 289           7-6 6-7 7-6  2.45  1.69  2.31 1.58             0.30550989
## 290           3-6 7-6 7-6  2.44  1.65  2.29 1.60             0.34592086
## 291   6-4 6-4 3-6 6-7 6-4  2.44  1.69  2.31 1.62             0.12610646
## 292               7-6 6-4  2.43  1.64  2.33 1.58             0.23813523
## 293               6-3 6-4  2.42  1.66  2.32 1.60             0.37732078
## 294               7-6 6-2  2.40  1.80  2.13 1.69             0.14634587
## 295           6-3 6-3 6-2  2.40  1.77  2.21 1.65             0.24774650
## 296               6-1 6-1  2.40  1.70  2.26 1.61             0.06928503
## 297               6-3 7-6  2.40  1.77  2.21 1.63             0.19142516
## 298               6-2 7-6  2.40  1.74  2.25 1.61             0.15461493
## 299               6-4 6-2  2.40  1.77  2.11 1.70             0.12643448
## 300               6-3 6-0  2.40  1.72  2.18 1.65             0.29771229
## 301           6-4 6-7 6-3  2.40  1.70  2.28 1.60             0.13351721
## 302               6-3 6-0  2.40  1.71  2.21 1.64             0.68333558
## 303               6-4 6-1  2.40  1.80  2.22 1.65             0.28799023
## 304               6-4 7-6  2.38  1.70  2.26 1.61             0.29699800
## 305               6-3 6-0  2.38  1.74  2.20 1.64             0.30825102
## 306           7-6 4-6 6-1  2.38  1.71  2.20 1.64             0.32721805
## 307           7-5 3-6 6-3  2.38  1.72  2.23 1.64             0.27590671
## 308       6-3 6-4 1-6 6-3  2.38  1.71  2.24 1.63             0.65467321
## 309           6-2 5-7 6-1  2.38  1.73  2.18 1.66             0.37075095
## 310               7-6 6-4  2.37  1.83  2.04 1.75             0.58212402
## 311           6-2 3-6 6-0  2.36  1.70  2.22 1.63             0.14162331
## 312               6-3 6-0  2.35  1.73  2.18 1.66             0.20738515
## 313               6-3 6-2  2.35  1.81  2.13 1.68             0.30039488
## 314               6-2 6-0  2.35  1.83  2.18 1.66             0.23269903
## 315           7-5 6-7 7-6  2.35  1.74  2.18 1.66             0.30296697
## 316               6-3 6-4  2.35  1.74  2.17 1.66             0.20756433
## 317               7-6 6-4  2.35  1.77  2.15 1.68             0.07771001
## 318               6-3 6-2  2.35  1.79  2.19 1.65             0.47460342
## 319               6-3 6-3  2.35  1.75  2.20 1.64             0.35675979
## 320           6-3 6-4 6-4  2.35  1.75  2.18 1.66             0.79905546
## 321           6-3 6-4 7-6  2.35  1.74  2.20 1.67             0.36990069
## 322               6-4 6-4  2.35  1.74  2.16 1.66             0.11766803
## 323               7-6 6-2  2.35  1.71  2.22 1.65             0.14619277
## 324           5-7 7-6 6-4  2.35  1.75  2.17 1.68             0.27929475
## 325           7-6 4-6 6-3  2.34  1.74  2.19 1.66             0.43519544
## 326               6-1 6-2  2.33  1.80  2.12 1.70             0.08550730
## 327               6-4 6-2  2.33  1.73  2.17 1.67             0.42796455
## 328           6-7 6-3 7-6  2.33  1.71  2.20 1.65             0.47349132
## 329               7-6 7-6  2.30  1.73  2.20 1.66             0.25019821
## 330           5-7 7-6 6-3  2.30  1.73  2.23 1.63             0.25522361
## 331           5-7 6-3 6-4  2.30  1.84  2.14 1.68             0.17506511
## 332           3-6 7-5 7-6  2.30  2.10  2.05 1.74             0.20128802
## 333               6-4 6-4  2.30  1.77  2.13 1.69             0.16000027
## 334           4-6 7-6 6-4  2.30  1.72  2.18 1.66             0.19776088
## 335               7-6 6-3  2.30  1.73  2.19 1.66             0.32025654
## 336           2-6 6-3 6-2  2.29  1.75  2.15 1.67             0.11927746
## 337               7-6 6-4  2.29  1.73  2.16 1.67             0.15179917
## 338           5-7 6-3 6-0  2.26  1.80  2.13 1.70             0.66152007
## 339           7-5 7-6 7-5  2.26  1.80  2.15 1.70             0.36165042
## 340           4-6 6-1 6-2  2.25  1.83  2.04 1.74             0.23825260
## 341               6-0 6-2  2.25  1.80  2.10 1.70             0.33874212
## 342           5-7 6-1 7-6  2.25  1.85  2.09 1.71             0.67383115
## 343               6-3 6-4  2.25  1.80  2.06 1.73             0.11267773
## 344           6-3 6-4 6-4  2.23  1.80  2.13 1.71             0.25165345
## 345           6-7 7-6 7-6  2.22  1.82  2.06 1.74             0.13388822
## 346               6-3 6-2  2.22  1.82  2.09 1.71             0.18295796
## 347               6-4 6-3  2.22  1.84  2.11 1.71             0.14372429
## 348               6-1 6-1  2.22  1.83  2.06 1.73             0.31741603
## 349               7-5 6-3  2.20  1.80  2.08 1.72             0.40352311
## 350           6-3 6-2 6-3  2.20  1.82  2.07 1.74             0.10058046
## 351           1-6 6-1 7-6  2.20  1.83  2.14 1.69             0.36206282
## 352           6-3 3-6 6-3  2.20  1.83  2.07 1.74             0.07715563
## 353               6-3 6-1  2.20  1.80  2.09 1.74             0.22055952
## 354           6-7 7-5 6-4  2.20  2.00  1.94 1.84             0.12799781
## 355               6-3 6-4  2.20  1.83  2.07 1.74             0.20086389
## 356           6-7 6-4 6-3  2.20  1.81  2.08 1.73             0.21443907
## 357               7-6 6-1  2.20  1.95  2.02 1.79             0.26256637
## 358           7-6 6-7 7-6  2.20  1.94  2.04 1.75             0.09725574
## 359               6-3 6-3  2.20  1.79  2.12 1.69             0.39223105
## 360               7-6 6-1  2.20  1.77  2.08 1.72             0.13954847
## 361       7-6 4-6 6-1 6-4  2.18  1.81  2.05 1.74             0.15063373
## 362           4-6 6-1 6-4  2.17  1.82  2.07 1.73             0.12213735
## 363               6-4 6-4  2.17  1.88  1.96 1.80             0.47709925
## 364               7-6 6-4  2.16  1.87  1.98 1.78             0.13591402
## 365           7-6 2-6 7-5  2.15  1.91  1.96 1.81             0.49670470
## 366   6-7 7-6 7-6 4-6 7-5  2.15  1.83  2.07 1.74             0.46558878
## 367           3-6 6-3 6-4  2.15  1.91  2.00 1.77             0.17225481
## 368           7-5 3-6 6-4  2.15  1.82  2.02 1.76             0.47896709
## 369               6-2 6-4  2.15  1.83  2.05 1.74             0.12831338
## 370           3-6 7-6 6-4  2.15  1.85  1.98 1.82             0.23295438
## 371               6-2 6-1  2.14  1.83  2.03 1.75             0.53009151
## 372               6-3 6-2  2.13  1.86  2.00 1.78             0.33256109
## 373               6-1 6-4  2.13  1.85  2.03 1.76             0.21307878
## 374           5-7 7-6 7-6  2.13  1.96  1.95 1.81             0.16461507
## 375               6-3 6-3  2.13  1.85  2.03 1.76             0.30819820
## 376               6-3 6-4  2.13  1.85  2.01 1.77             0.22380547
## 377               6-4 6-1  2.12  1.91  1.97 1.80             0.10250308
## 378           7-6 6-4 6-4  2.11  1.85  2.00 1.78             0.16047818
## 379           4-6 6-2 6-2  2.11  1.95  1.96 1.81             0.26553483
## 380               7-6 7-5  2.10  1.90  1.96 1.80             0.27707386
## 381               7-6 7-6  2.10  1.92  1.93 1.83             0.11103231
## 382           3-6 6-4 6-3  2.10  1.90  1.99 1.78             0.19028215
## 383               6-4 6-3  2.10  1.86  2.01 1.76             0.07045321
## 384           1-6 6-2 7-5  2.10  2.00  1.94 1.83             0.47071106
## 385               7-6 7-5  2.10  1.85  2.01 1.77             0.11645529
## 386   5-7 6-2 6-4 0-6 6-2  2.10  1.96  1.95 1.84             0.35133371
## 387               7-6 6-4  2.10  1.87  2.02 1.76             0.08406655
## 388               7-6 6-3  2.10  1.82  2.01 1.77             0.13472170
## 389               6-3 6-4  2.10  1.92  1.96 1.81             0.39451137
## 390           6-3 4-6 7-6  2.10  1.92  1.96 1.81             0.29602210
## 391               6-2 6-3  2.10  2.05  1.89 1.89             0.30828634
## 392       7-6 5-7 7-5 6-3  2.10  2.02  1.87 1.90             0.19381626
## 393           7-6 6-7 6-4  2.10  1.90  1.95 1.82             0.39714951
## 394           6-4 6-7 6-3  2.10  2.19  1.79 1.99             0.48810602
## 395           6-7 6-4 6-3  2.10  1.99  1.96 1.81             0.39784207
## 396 5-7 6-3 6-4 6-7 13-11  2.10  1.83  2.03 1.77             0.15850820
## 397           6-4 1-6 7-5  2.10  1.87  1.97 1.80             0.12121766
## 398           7-6 7-5 7-5  2.09  2.00  1.95 1.82             0.40445811
## 399               7-5 6-4  2.09  1.95  1.93 1.84             0.33950979
## 400               6-3 6-2  2.08  2.00  1.94 1.82             0.12757068
## 401               6-4 6-1  2.06  2.00  1.88 1.88             0.18254534
## 402   6-2 6-2 4-6 2-6 7-6  2.06  1.92  1.93 1.84             0.32176034
## 403           4-6 6-1 7-6  2.05  1.91  1.94 1.82             0.16506403
## 404           7-6 3-6 6-3  2.05  1.95  1.92 1.84             0.31520415
## 405           6-1 4-6 6-3  2.05  1.92  1.94 1.83             0.37301745
## 406               6-2 7-6  2.05  1.93  1.93 1.82             0.08380806
## 407           6-3 6-3 6-3  2.05  1.94  1.96 1.85             0.29390802
## 408           3-6 7-5 7-6  2.05  1.91  1.94 1.82             0.09989514
## 409       6-2 3-6 6-4 6-2  2.05  2.09  1.84 1.94             0.09531459
## 410               6-3 6-4  2.04  1.91  1.91 1.85             0.36460752
## 411               6-3 6-4  2.03  2.04  1.90 1.86             0.12857277
## 412               7-6 6-4  2.03  1.95  1.91 1.85             0.20353251
## 413               6-3 6-4  2.03  1.93  1.93 1.83             0.19254393
## 414           4-6 6-0 6-3  2.02  2.00  1.87 1.91             0.28813149
## 415               6-4 6-3  2.02  1.91  1.93 1.83             0.36163918
## 416               7-5 6-3  2.01  2.00  1.90 1.86             0.09266542
## 417           7-5 3-6 6-4  2.00  2.00  1.89 1.87             0.15488036
## 418               6-4 6-4  2.00  2.05  1.87 1.89             0.14693102
## 419           6-1 1-6 6-4  2.00  2.15  1.84 1.92             0.10588607
## 420               6-3 7-6  2.00  2.05  1.86 1.90             0.43281063
## 421           6-7 6-4 6-4  2.00  1.98  1.89 1.86             0.11437955
## 422           6-7 7-6 6-4  2.00  2.05  1.90 1.87             0.10538633
## 423           4-6 6-4 6-0  2.00  2.12  1.83 1.91             0.29535311
## 424               6-1 6-4  2.00  2.00  1.88 1.92             0.21934972
## 425           4-6 6-3 7-5  2.00  1.95  1.91 1.87             0.13675501
## 426       7-6 6-7 6-4 6-3  2.00  2.10  1.91 1.96             0.08173468
## 427           6-4 4-6 6-3  2.00  2.00  1.87 1.89             0.10471129
## 428               6-4 7-6  2.00  1.94  1.91 1.86             0.10123093
## 429       4-6 6-1 7-6 6-3  1.99  2.10  1.83 1.96             0.13309619
## 430   6-1 6-7 3-6 7-6 8-6  1.97  2.02  1.84 1.92             0.29043387
## 431               6-2 7-5  1.97 13.25  1.05 9.61             0.78757079
## 432   4-6 4-6 7-6 7-6 6-4  1.97  2.15  1.74 2.06             0.09998566
## 433           7-5 4-6 6-2  1.96  1.96  1.87 1.89             0.07358953
## 434               6-4 6-4  1.96  2.00  1.87 1.88             0.09235133
## 435           6-7 7-5 7-6  1.95  2.10  1.85 1.90             0.27642091
## 436               6-2 7-5  1.95  2.05  1.84 1.92             0.10467500
## 437           2-6 6-3 6-3  1.95  2.00  1.83 1.92             0.20863103
## 438               7-6 6-4  1.95  2.00  1.88 1.88             0.12950765
## 439           6-3 3-6 6-3  1.95  1.97  1.87 1.88             0.44282155
## 440               6-3 6-4  1.95  2.02  1.85 1.91             0.40494143
## 441               6-1 6-3  1.95  2.04  1.86 1.92             0.10216664
## 442           7-6 4-6 6-3  1.95  2.05  1.86 1.91             0.25544051
## 443               6-2 6-3  1.94  2.19  1.80 1.97             0.17783454
## 444           6-3 3-6 7-5  1.94  2.03  1.85 1.91             0.41043695
## 445           4-6 6-2 7-5  1.93  2.06  1.84 1.91             0.07911507
## 446               6-3 7-5  1.93  2.02  1.85 1.92             0.06722731
## 447           6-3 3-6 6-3  1.93  2.11  1.81 1.96             0.20361938
## 448               7-5 6-4  1.92  2.04  1.85 1.90             0.19222212
## 449               7-6 6-4  1.92  2.05  1.83 1.93             0.15654391
## 450           6-3 6-7 6-3  1.91  2.10  1.79 1.98             0.13684402
## 451           6-3 4-6 6-4  1.91  2.12  1.82 1.93             0.18897377
## 452   3-6 2-6 7-6 7-5 6-4  1.91  2.13  1.83 1.95             0.11050428
## 453               6-2 6-4  1.91  2.20  1.79 1.99             0.17531490
## 454               7-5 6-1  1.91  2.10  1.80 1.98             0.13794423
## 455           6-3 7-6 6-1  1.91  2.20  1.76 2.06             0.34017645
## 456               6-3 6-4  1.91  2.04  1.85 1.93             0.09799620
## 457               6-3 7-6  1.90  2.12  1.78 2.00             0.14897658
## 458           6-7 7-6 7-6  1.89  2.16  1.82 1.96             0.22832518
## 459           5-7 6-3 6-2  1.88  2.16  1.75 2.04             0.12575192
## 460           4-6 6-1 6-3  1.88  2.30  1.71 2.10             0.50434914
## 461               6-4 6-4  1.88  2.18  1.75 2.04             0.28215658
## 462               6-2 6-1  1.88  2.10  1.77 2.03             0.35758608
## 463               7-6 6-2  1.87  2.14  1.77 1.99             0.14743905
## 464           7-6 5-7 6-4  1.86  2.30  1.69 2.12             0.06916172
## 465           7-6 3-6 6-4  1.86  2.14  1.77 2.01             0.07134943
## 466           4-6 6-2 6-2  1.85  2.10  1.77 2.02             0.15330899
## 467               6-3 6-4  1.85  2.12  1.79 1.99             0.15653688
## 468           1-6 6-3 6-2  1.85  2.12  1.77 2.02             0.06225428
## 469               6-4 6-3  1.85  2.25  1.72 2.10             0.20995201
## 470               6-4 6-4  1.85  2.20  1.75 2.06             0.13446107
## 471               6-4 7-5  1.85  2.16  1.76 2.01             0.20162059
## 472           6-3 6-7 7-6  1.85  2.27  1.70 2.13             0.16435396
## 473           7-6 6-7 6-3  1.84  2.15  1.75 2.03             0.21048315
## 474               6-3 6-2  1.84  2.30  1.74 2.07             0.20678834
## 475           6-7 7-5 6-4  1.84  2.30  1.72 2.09             0.38470637
## 476           7-6 5-7 6-4  1.84  2.22  1.75 2.07             0.22315053
## 477           6-4 6-1 7-6  1.83  2.20  1.73 2.08             0.13077105
## 478               6-4 6-4  1.83  2.25  1.73 2.06             0.37459362
## 479               6-1 6-4  1.83  2.18  1.75 2.05             0.29622468
## 480               7-5 6-3  1.83  2.15  1.74 2.06             0.16139218
## 481           7-6 6-7 7-6  1.83  2.47  1.72 2.11             0.26926229
## 482           6-7 7-5 6-2  1.83  2.20  1.74 2.05             0.14696971
## 483               6-4 7-6  1.83  2.17  1.76 2.02             0.15599286
## 484               6-1 7-5  1.81  2.50  1.60 2.31             0.24500403
## 485               7-6 6-4  1.81  2.26  1.72 2.08             0.09528304
## 486               7-6 6-4  1.80  2.36  1.73 2.06             0.22829584
## 487               6-4 6-3  1.80  2.35  1.69 2.14             0.18642867
## 488               6-1 7-6  1.80  2.25  1.70 2.11             0.16797696
## 489           6-2 3-6 6-3  1.80  2.38  1.65 2.21             0.15217065
## 490               6-3 7-6  1.80  2.25  1.72 2.07             0.18488539
## 491           7-5 7-5 6-4  1.80  2.35  1.69 2.17             0.33979199
## 492           5-7 6-4 6-4  1.80  2.30  1.69 2.15             0.23008257
## 493       6-4 4-6 6-4 6-0  1.80  2.42  1.64 2.23             0.19518593
## 494               6-3 6-4  1.80  2.15  1.74 2.03             0.23822958
## 495           6-4 3-6 7-6  1.80  2.14  1.74 2.05             0.15403248
## 496           6-3 6-7 6-4  1.80  2.29  1.66 2.17             0.08554649
## 497 7-6 6-7 6-4 6-7 12-10  1.80  2.38  1.69 2.15             0.15542452
## 498           6-3 1-6 6-4  1.79  2.50  1.60 2.30             0.13343690
## 499           1-6 6-4 7-5  1.79  2.45  1.65 2.19             0.10427393
## 500           4-6 6-3 6-3  1.79  2.25  1.71 2.12             0.29139206
## 501           6-4 3-6 6-3  1.78  2.50  1.66 2.19             0.10059019
## 502           6-2 4-6 6-3  1.78  2.25  1.70 2.12             0.20266215
## 503   6-7 6-2 6-1 6-7 6-2  1.78  2.40  1.66 2.19             0.19791970
## 504               6-2 6-2  1.77  2.38  1.65 2.19             0.30605226
## 505           3-6 6-4 6-3  1.77  2.35  1.67 2.19             0.25928774
## 506               6-3 6-4  1.77  2.30  1.67 2.16             0.06364945
## 507       6-4 7-5 2-6 7-6  1.77  2.30  1.69 2.14             0.28924982
## 508               7-6 6-1  1.77  2.25  1.68 2.15             0.14238662
## 509               6-3 6-3  1.77  2.44  1.61 2.28             0.24566628
## 510               6-3 6-4  1.77  2.25  1.70 2.11             0.28879882
## 511               6-4 6-4  1.77  2.40  1.63 2.25             0.20990418
## 512               6-3 6-2  1.76  2.31  1.67 2.20             0.26136168
## 513               6-3 6-2  1.76  2.23  1.70 2.11             0.21252090
## 514       6-4 5-7 6-4 6-4  1.76  2.30  1.70 2.17             0.09480880
## 515           2-6 6-4 6-4  1.76  2.25  1.69 2.12             0.23826273
## 516       6-2 4-6 6-4 6-4  1.75  2.30  1.66 2.20             0.09223147
## 517       3-6 7-5 6-2 6-4  1.75  2.50  1.68 2.23             0.27992580
## 518       6-7 6-0 6-3 7-5  1.75  2.30  1.69 2.18             0.21310270
## 519           6-3 6-7 6-4  1.75  2.52  1.62 2.24             0.10601298
## 520           6-2 5-7 6-3  1.75  2.40  1.64 2.22             0.24541361
## 521               6-4 6-4  1.75  2.33  1.68 2.16             0.13407561
## 522               6-3 6-3  1.74  2.35  1.69 2.18             0.07772110
## 523               6-2 6-2  1.74  2.50  1.61 2.27             0.14669048
## 524               6-4 7-5  1.74  2.31  1.68 2.17             0.14085727
## 525           6-3 1-6 6-4  1.74  2.50  1.64 2.20             0.40238942
## 526               6-3 7-6  1.74  2.33  1.63 2.21             0.16453644
## 527           1-6 6-2 6-4  1.74  2.38  1.64 2.23             0.15552089
## 528           3-6 6-3 6-2  1.73  2.40  1.63 2.24             0.17683870
## 529           6-4 7-5 7-6  1.73  2.38  1.63 2.25             0.11896540
## 530           2-6 7-6 6-4  1.73  2.30  1.65 2.20             0.24302254
## 531           6-3 6-2 6-2  1.73  2.33  1.65 2.20             0.09024009
## 532               6-3 6-0  1.73  2.35  1.66 2.22             0.30559892
## 533               6-3 6-3  1.72  2.30  1.65 2.20             0.18079289
## 534           7-6 6-4 6-4  1.71  2.40  1.63 2.25             0.16888396
## 535               6-3 6-4  1.71  2.40  1.65 2.20             0.16571590
## 536               6-4 7-6  1.71  2.50  1.59 2.33             0.22223937
## 537           3-6 6-4 6-4  1.71  2.38  1.63 2.22             0.12388351
## 538               6-3 7-5  1.71  2.55  1.58 2.33             0.15157524
## 539               6-2 7-5  1.70  2.55  1.55 2.40             0.13230692
## 540           6-1 4-6 6-3  1.70  2.35  1.63 2.24             0.18150750
## 541               7-5 6-2  1.70  2.37  1.63 2.25             0.21930227
## 542               6-4 6-1  1.70  2.50  1.61 2.29             0.12470043
## 543           7-6 6-7 6-1  1.70  2.34  1.65 2.19             0.07371321
## 544           6-4 6-7 7-6  1.70  2.42  1.59 2.32             0.10859987
## 545           3-6 6-3 6-3  1.69  2.50  1.56 2.38             0.06489687
## 546               6-4 6-3  1.69  2.50  1.61 2.28             0.18353580
## 547           7-6 6-4 6-4  1.69  2.55  1.61 2.29             0.16307552
## 548               6-3 6-4  1.69  2.45  1.60 2.29             0.13580164
## 549           6-3 6-7 6-2  1.69  2.63  1.57 2.40             0.15549547
## 550               6-3 6-3  1.69  2.41  1.61 2.30             0.12823083
## 551               7-5 6-2  1.68  2.35  1.62 2.26             0.06741993
## 552           6-4 3-6 6-3  1.68  2.40  1.62 2.24             0.24169242
## 553           4-6 6-2 6-3  1.68  2.63  1.59 2.31             0.30625561
## 554               7-5 6-2  1.68  2.60  1.55 2.39             0.16817021
## 555           6-3 6-2 6-4  1.68  2.40  1.62 2.29             0.25613357
## 556           6-3 7-5 6-4  1.67  2.50  1.59 2.34             0.30751021
## 557               6-3 6-2  1.67  2.40  1.61 2.26             0.18704453
## 558               7-5 7-6  1.67  2.50  1.58 2.35             0.10507479
## 559               6-3 6-4  1.67  2.62  1.55 2.39             0.16993159
## 560               7-6 6-3  1.67  2.44  1.59 2.31             0.12104020
## 561               6-4 7-5  1.67  2.55  1.58 2.35             0.20700866
## 562           6-4 6-7 6-3  1.67  2.55  1.57 2.38             0.19935801
## 563           3-6 6-1 6-3  1.66  2.50  1.57 2.35             0.18126632
## 564               6-4 6-4  1.66  2.50  1.58 2.33             0.07586253
## 565           6-1 6-2 7-6  1.66  2.65  1.57 2.38             0.12485879
## 566       6-3 2-6 6-4 7-6  1.66  2.60  1.55 2.42             0.21787560
## 567   3-6 6-3 3-6 6-3 6-4  1.65  2.45  1.59 2.31             0.33728263
## 568               6-2 6-1  1.65  2.55  1.56 2.38             0.07595886
## 569               7-6 6-3  1.65  2.53  1.57 2.34             0.08536894
## 570               6-1 6-2  1.65  2.60  1.57 2.36             0.21739923
## 571               6-4 7-5  1.65  2.55  1.57 2.36             0.14081782
## 572           6-4 6-4 6-0  1.65  2.60  1.56 2.43             0.10201380
## 573               6-3 7-6  1.65  2.70  1.54 2.44             0.22698411
## 574           6-4 6-3 6-4  1.63  2.65  1.55 2.44             0.16951819
## 575               6-2 7-6  1.63  2.65  1.56 2.38             0.15975778
## 576               6-3 6-3  1.63  2.75  1.50 2.52             0.09266362
## 577           6-3 6-7 6-2  1.63  2.62  1.52 2.48             0.07897528
## 578               6-4 6-4  1.63  2.50  1.55 2.39             0.11396451
## 579               7-5 6-4  1.62  2.62  1.54 2.44             0.16119395
## 580               6-3 6-4  1.62  2.70  1.53 2.44             0.10029152
## 581               6-3 6-4  1.62  2.67  1.55 2.38             0.39455877
## 582           6-4 3-6 6-3  1.62  2.80  1.54 2.46             0.21316308
## 583           6-2 5-7 6-2  1.62  2.50  1.56 2.37             0.08067186
## 584               6-4 7-5  1.62  2.63  1.53 2.47             0.17734624
## 585       6-4 7-6 4-6 6-4  1.62  2.55  1.54 2.42             0.10361023
## 586               7-5 6-4  1.62  2.70  1.52 2.50             0.09756791
## 587           6-4 6-7 6-1  1.61  2.55  1.55 2.43             0.10704987
## 588               7-5 7-5  1.61  2.65  1.52 2.49             0.20912554
## 589               6-4 6-1  1.61  2.60  1.54 2.41             0.16258790
## 590           6-7 7-6 7-6  1.61  2.60  1.54 2.46             0.09121684
## 591               6-3 7-6  1.60  2.80  1.51 2.51             0.10690637
## 592           6-3 6-7 6-4  1.60  2.70  1.52 2.50             0.09700591
## 593           6-3 2-6 6-3  1.60  2.75  1.50 2.54             0.28612689
## 594               7-6 6-3  1.60  2.62  1.54 2.40             0.08956852
## 595               7-6 6-3  1.60  2.70  1.50 2.53             0.09515842
## 596               6-3 7-6  1.60  2.75  1.53 2.46             0.14322707
## 597               6-3 6-2  1.59  2.70  1.51 2.53             0.17261572
## 598               6-4 7-5  1.59  2.74  1.52 2.48             0.15867500
## 599           5-7 6-3 7-6  1.59  2.62  1.52 2.49             0.15416127
## 600           3-6 6-0 6-3  1.59  2.55  1.54 2.39             0.12183742
## 601   6-4 6-1 4-6 1-6 6-0  1.58  2.75  1.51 2.56             0.15715820
## 602           4-6 7-6 6-3  1.58  2.69  1.53 2.47             0.07693085
## 603               6-3 6-4  1.58  2.65  1.52 2.47             0.16470723
## 604               7-6 6-4  1.57  2.82  1.49 2.57             0.23788599
## 605               6-4 6-1  1.57  2.65  1.49 2.55             0.09458389
## 606               6-3 6-3  1.57  2.76  1.49 2.58             0.27144454
## 607               6-3 7-5  1.57  2.83  1.50 2.59             0.18126861
## 608           4-6 6-2 6-1  1.57  2.85  1.50 2.51             0.07655692
## 609               6-1 6-4  1.57  2.60  1.53 2.46             0.18407600
## 610               7-5 7-5  1.57  2.70  1.51 2.52             0.19418297
## 611               7-5 6-4  1.56  2.75  1.50 2.52             0.15090131
## 612           6-7 7-6 7-6  1.56  2.95  1.46 2.67             0.08539805
## 613               7-6 6-2  1.56  2.75  1.52 2.49             0.09529775
## 614               6-3 6-2  1.56  2.75  1.49 2.58             0.15469560
## 615               7-5 6-3  1.56  2.85  1.47 2.63             0.13289098
## 616   6-2 6-7 3-6 6-4 6-4  1.56  2.70  1.52 2.48             0.24019251
## 617               7-6 6-3  1.56  2.74  1.48 2.60             0.13134908
## 618               6-2 6-4  1.56  2.75  1.48 2.62             0.07807274
## 619               6-4 6-4  1.56  2.66  1.51 2.52             0.24414498
## 620           6-2 4-6 6-4  1.55  3.00  1.48 2.65             0.20255066
## 621               6-2 6-2  1.55  2.73  1.47 2.59             0.08115293
## 622               6-3 7-6  1.54  2.80  1.48 2.62             0.30842283
## 623               7-6 6-3  1.54  2.68  1.49 2.55             0.07704486
## 624           6-2 3-6 6-3  1.54  2.90  1.43 2.72             0.14774069
## 625       6-3 2-6 7-6 6-1  1.54  2.87  1.50 2.60             0.19981711
## 626           2-6 6-3 6-4  1.54  2.75  1.47 2.64             0.21292658
## 627               7-6 6-2  1.54  3.06  1.45 2.74             0.20353119
## 628               6-2 6-4  1.53  2.90  1.47 2.62             0.07408701
## 629           1-6 7-5 6-4  1.53  3.35  1.42 2.85             0.12435944
## 630           4-6 7-6 6-4  1.53  3.26  1.41 2.84             0.30151169
## 631               7-6 6-3  1.53  2.75  1.49 2.54             0.09349383
## 632           4-6 6-3 6-4  1.53  3.30  1.39 2.93             0.12800206
## 633           3-6 6-4 6-3  1.53  2.88  1.45 2.68             0.33927060
## 634               7-5 6-3  1.53  3.10  1.46 2.70             0.42915851
## 635           6-4 4-6 6-3  1.53  3.05  1.47 2.65             0.22310880
## 636               6-3 6-2  1.52  3.00  1.44 2.76             0.23643437
## 637               7-6 6-0  1.52  3.25  1.44 2.76             0.10211098
## 638       5-7 6-2 6-4 6-4  1.52  2.90  1.45 2.72             0.17152073
## 639           6-3 3-6 6-1  1.51  2.90  1.43 2.71             0.14079089
## 640   7-6 6-7 6-4 3-6 6-2  1.51  3.00  1.44 2.73             0.16939040
## 641               7-6 6-2  1.51  2.80  1.46 2.66             0.07908737
## 642           4-6 6-3 6-3  1.50  3.05  1.44 2.70             0.13741279
## 643               7-6 6-3  1.50  3.16  1.41 2.83             0.09985490
## 644               7-6 6-3  1.50  3.01  1.44 2.76             0.24945386
## 645               6-2 6-3  1.50  2.95  1.42 2.79             0.13988589
## 646           6-3 3-6 6-3  1.50  2.95  1.45 2.69             0.08615514
## 647               6-3 6-4  1.50  2.95  1.43 2.74             0.07098038
## 648               6-2 6-3  1.50  3.20  1.43 2.82             0.19950119
## 649               6-4 7-6  1.50  2.97  1.44 2.71             0.14228372
## 650               7-6 6-3  1.50  2.92  1.44 2.68             0.12910453
## 651               7-6 6-2  1.50  3.00  1.43 2.76             0.12216951
## 652               7-5 6-2  1.50  3.10  1.43 2.76             0.21466861
## 653           7-5 6-7 7-6  1.50  3.00  1.43 2.74             0.26975325
## 654               6-3 7-6  1.50  2.90  1.47 2.64             0.09257630
## 655 3-6 6-3 6-3 4-6 12-10  1.49  3.06  1.43 2.80             0.12959073
## 656       7-5 4-6 7-6 6-2  1.49  3.20  1.45 2.76             0.07144538
## 657               6-4 7-6  1.49  3.50  1.39 2.94             0.09907423
## 658               6-1 6-4  1.48  3.45  1.40 2.89             0.07332494
## 659               6-3 6-4  1.48  2.86  1.44 2.73             0.10095092
## 660           6-7 6-4 7-6  1.48  3.00  1.42 2.80             0.20897649
## 661               7-6 6-3  1.48  3.30  1.39 2.92             0.17796033
## 662               6-3 6-1  1.47  3.34  1.39 2.90             0.16519886
## 663               6-2 6-4  1.47  3.40  1.38 2.94             0.11692189
## 664           6-4 6-4 6-4  1.47  3.40  1.38 3.06             0.27369653
## 665               7-6 6-4  1.47  3.16  1.41 2.87             0.10365550
## 666           4-6 6-3 7-6  1.47  3.09  1.41 2.81             0.22945644
## 667           4-6 6-3 6-3  1.46  3.25  1.38 2.94             0.18463488
## 668       6-3 6-2 3-6 7-6  1.45  3.65  1.39 2.93             0.06509078
## 669               6-1 6-2  1.45  3.25  1.38 2.97             0.14641475
## 670           6-3 3-6 7-6  1.45  3.36  1.37 3.05             0.08854643
## 671       3-6 6-3 7-6 6-1  1.45  3.11  1.41 2.88             0.07592657
## 672           5-7 6-3 6-1  1.44  3.41  1.38 2.97             0.09037908
## 673           7-5 6-2 6-3  1.44  3.40  1.37 3.08             0.08459433
## 674               7-6 6-4  1.44  3.39  1.37 3.02             0.19630404
## 675           6-7 7-6 7-6  1.44  3.20  1.39 2.93             0.07785094
## 676           5-7 6-3 6-2  1.44  3.14  1.38 2.93             0.14057729
## 677               6-1 7-6  1.44  3.05  1.40 2.86             0.07125886
## 678           4-6 6-1 6-4  1.44  3.65  1.36 3.12             0.07073154
## 679               6-3 6-3  1.44  3.32  1.36 3.03             0.09158387
## 680           4-6 6-2 6-3  1.43  3.45  1.36 3.05             0.08107356
## 681               6-4 6-2  1.42  3.50  1.34 3.24             0.19313726
## 682   4-6 6-7 7-5 6-4 6-3  1.42  3.30  1.35 3.13             0.14406348
## 683               6-1 6-4  1.42  3.40  1.36 3.03             0.13943567
## 684               6-1 6-2  1.42  3.30  1.36 3.01             0.22201095
## 685           4-6 7-6 7-6  1.42  3.50  1.34 3.14             0.07797845
## 686           6-4 5-7 6-2  1.42  3.45  1.35 3.15             0.10818795
## 687               7-5 6-3  1.42  3.25  1.35 3.11             0.08765739
## 688       7-6 6-4 3-6 6-3  1.42  3.25  1.36 3.08             0.18633605
## 689               6-3 6-2  1.41  3.40  1.36 3.07             0.13073978
## 690           3-6 7-6 6-2  1.41  3.40  1.36 3.09             0.10407828
## 691               6-1 6-2  1.41  3.45  1.34 3.14             0.08390741
## 692           3-6 6-3 6-1  1.41  3.38  1.36 3.05             0.11921398
## 693           7-5 5-7 6-4  1.41  3.40  1.36 3.04             0.18148597
## 694           6-2 7-6 6-2  1.40  3.70  1.33 3.27             0.18993581
## 695               6-4 6-3  1.40  3.43  1.34 3.22             0.23895951
## 696               6-2 6-3  1.40  3.36  1.35 3.10             0.16615694
## 697           7-5 6-3 6-4  1.40  3.40  1.34 3.18             0.24959093
## 698           0-6 6-2 6-1  1.40  3.50  1.35 3.13             0.11201721
## 699           1-6 6-3 6-3  1.40  3.55  1.31 3.37             0.10511623
## 700           6-4 4-6 6-3  1.40  3.25  1.36 3.09             0.12145469
## 701               6-3 6-2  1.40  3.90  1.35 3.19             0.06580341
## 702               6-4 6-4  1.40  3.67  1.33 3.21             0.13163183
## 703           6-4 3-6 6-1  1.40  3.75  1.32 3.33             0.09439518
## 704               6-2 6-3  1.40  3.50  1.33 3.24             0.14332058
## 705           6-4 6-4 7-6  1.40  3.46  1.34 3.20             0.18782901
## 706               6-2 6-0  1.40  3.40  1.34 3.18             0.13269994
## 707           6-3 5-7 7-5  1.40  3.35  1.36 3.08             0.07840781
## 708           7-6 4-6 6-4  1.40  3.22  1.37 3.01             0.09411927
## 709       6-3 4-6 6-4 6-1  1.39  3.75  1.33 3.29             0.09204578
## 710               6-3 6-4  1.38  3.70  1.31 3.39             0.10429562
## 711               6-3 6-4  1.38  3.57  1.33 3.25             0.11980886
## 712               6-1 7-6  1.38  3.75  1.33 3.30             0.09092594
## 713               7-6 7-6  1.38  3.65  1.33 3.25             0.15191324
## 714           1-6 6-4 6-4  1.38  3.50  1.33 3.23             0.22549538
## 715               7-6 6-1  1.37  3.52  1.33 3.26             0.27050722
## 716               6-2 7-5  1.37  3.55  1.32 3.27             0.16581883
## 717               6-3 6-4  1.37  3.56  1.32 3.30             0.17703500
## 718           6-2 7-6 6-2  1.37  3.85  1.31 3.45             0.14287437
## 719           6-7 6-3 6-3  1.37  3.55  1.32 3.29             0.14133457
## 720           6-3 7-6 6-2  1.36  3.70  1.32 3.33             0.12387201
## 721           4-6 6-3 6-2  1.36  3.65  1.31 3.39             0.08972469
## 722               6-3 6-4  1.36  3.70  1.33 3.24             0.09434871
## 723           6-2 6-2 6-4  1.36  4.00  1.32 3.37             0.10682925
## 724           6-4 6-3 6-4  1.36  3.80  1.30 3.51             0.14026866
## 725               6-4 6-3  1.35  3.85  1.28 3.55             0.06807195
## 726           6-3 5-7 6-2  1.35  4.35  1.30 3.48             0.07695002
## 727               6-3 6-1  1.35  3.67  1.30 3.42             0.21908469
## 728       3-6 7-6 6-4 6-4  1.35  4.00  1.30 3.58             0.14003955
## 729               6-2 6-3  1.35  3.77  1.30 3.36             0.08397580
## 730               7-6 6-1  1.35  3.90  1.30 3.54             0.19668491
## 731               6-3 6-1  1.34  4.10  1.28 3.63             0.18300515
## 732           4-6 7-6 6-2  1.34  3.75  1.31 3.43             0.08729980
## 733           7-5 6-1 6-4  1.34  4.01  1.29 3.54             0.18858594
## 734   4-6 3-6 6-3 7-5 6-2  1.34  3.83  1.30 3.45             0.21031332
## 735           6-4 6-3 6-1  1.34  3.91  1.31 3.50             0.09553535
## 736               6-2 6-1  1.33  4.55  1.25 3.78             0.07416136
## 737               6-2 6-1  1.33  4.33  1.25 3.81             0.17761380
## 738           6-2 7-6 7-6  1.33  4.00  1.27 3.71             0.16969465
## 739               7-5 6-3  1.33  4.39  1.28 3.61             0.06090284
## 740           5-7 7-6 6-1  1.33  3.88  1.30 3.49             0.11903824
## 741           6-3 5-7 6-3  1.33  3.70  1.29 3.46             0.07443117
## 742               6-3 6-2  1.33  4.20  1.27 3.66             0.09983751
## 743           7-6 6-2 6-2  1.33  3.79  1.30 3.47             0.08568377
## 744               6-3 6-4  1.33  3.90  1.27 3.66             0.08426201
## 745               6-4 6-4  1.32  4.33  1.25 3.84             0.13338561
## 746       6-4 3-6 7-6 7-6  1.32  4.45  1.25 3.98             0.21115382
## 747               6-2 6-2  1.32  3.95  1.27 3.68             0.10804211
## 748       6-4 6-7 6-3 7-5  1.32  3.90  1.29 3.57             0.12817916
## 749               6-3 7-6  1.32  4.50  1.26 3.84             0.11501484
## 750               6-3 6-4  1.31  3.90  1.27 3.66             0.07393036
## 751               6-3 6-1  1.31  4.15  1.27 3.65             0.13908650
## 752               6-3 6-4  1.31  4.40  1.25 3.87             0.15982861
## 753               6-4 6-1  1.31  4.15  1.27 3.77             0.09352158
## 754               7-5 7-5  1.30  5.00  1.23 4.07             0.12016458
## 755           6-2 6-1 7-5  1.30  5.17  1.23 4.16             0.11970141
## 756   4-6 3-6 6-4 7-5 6-2  1.30  4.33  1.25 3.93             0.11017262
## 757               6-2 6-2  1.30  5.00  1.21 4.24             0.23220127
## 758   7-6 3-6 6-4 4-6 6-0  1.30  4.70  1.23 4.26             0.15552711
## 759               6-2 6-3  1.30  4.20  1.25 3.84             0.13098870
## 760               7-6 6-4  1.30  4.15  1.26 3.76             0.15741062
## 761               6-2 6-2  1.29  4.60  1.25 3.89             0.22688816
## 762               6-2 6-1  1.29  4.33  1.25 3.81             0.06164924
## 763           3-6 7-6 7-6  1.29  4.50  1.23 4.05             0.08176826
## 764               6-2 6-1  1.28  4.32  1.24 3.91             0.07413036
## 765               6-4 6-2  1.28  4.31  1.25 3.94             0.11815355
## 766               6-3 6-4  1.27  4.52  1.23 3.97             0.07276501
## 767               7-6 7-6  1.27  4.60  1.24 4.03             0.06511402
## 768               7-6 6-2  1.27  4.40  1.24 3.91             0.07136135
## 769               6-3 7-5  1.26  4.84  1.21 4.15             0.13075630
## 770           4-6 7-6 7-6  1.26  4.80  1.22 4.22             0.07450910
## 771               6-4 6-2  1.26  5.00  1.19 4.57             0.07956234
## 772               6-4 6-1  1.25  4.80  1.21 4.33             0.07126045
## 773               6-2 6-2  1.25  4.72  1.22 4.09             0.08897404
## 774           7-6 1-6 6-3  1.24  4.75  1.20 4.38             0.06566982
## 775               6-2 6-3  1.24  5.10  1.20 4.56             0.08212660
## 776               6-2 6-4  1.23  5.20  1.19 4.60             0.09636665
## 777               6-2 6-2  1.23  5.60  1.18 4.73             0.12676118
## 778           7-5 6-7 6-1  1.22  5.50  1.17 4.95             0.09009467
## 779               6-0 6-2  1.22  5.50  1.17 4.86             0.09507557
## 780               6-3 6-4  1.22  5.50  1.18 4.85             0.09752878
## 781           6-3 6-2 7-6  1.22  5.40  1.19 4.62             0.09771001
## 782               6-3 7-6  1.22  5.60  1.17 4.73             0.07623877
## 783               6-3 6-4  1.22  5.46  1.19 4.66             0.15087973
## 784               6-4 6-1  1.21  5.68  1.16 5.01             0.06189564
## 785               7-6 6-0  1.21  5.50  1.18 4.78             0.07268338
## 786               6-4 6-4  1.21  5.23  1.18 4.67             0.08830582
## 787               7-5 7-5  1.21  5.50  1.17 4.94             0.16931535
## 788               6-3 7-6  1.20  5.77  1.16 5.18             0.16880314
## 789           6-3 6-2 6-1  1.20  7.75  1.13 6.13             0.09465456
## 790           6-2 6-2 7-5  1.20  6.00  1.16 5.16             0.07985984
## 791               6-4 6-2  1.20  5.75  1.17 4.96             0.06679410
## 792           6-4 6-7 6-2  1.20  5.50  1.16 4.96             0.06700832
## 793               6-2 6-2  1.20  5.83  1.17 5.00             0.12516392
## 794               7-6 6-2  1.20  5.96  1.16 5.10             0.07703767
## 795               6-3 6-2  1.20  5.57  1.16 4.98             0.15493544
## 796               7-6 7-5  1.18  6.16  1.15 5.19             0.07316199
## 797               6-4 6-4  1.18  6.50  1.13 5.71             0.13537854
## 798           3-6 6-1 6-1  1.18  6.42  1.15 5.26             0.08391655
## 799           1-6 7-5 7-6  1.17  6.09  1.14 5.49             0.10516915
## 800           7-6 6-4 6-2  1.15  9.50  1.10 6.75             0.07084861
## 801       6-3 6-3 3-6 6-3  1.15  7.85  1.12 6.52             0.07479169
## 802           7-6 5-7 6-2  1.15  6.75  1.13 5.78             0.07024437
## 803               6-4 6-2  1.15 10.00  1.09 7.05             0.07730134
## 804           7-6 4-6 6-3  1.15  8.40  1.11 6.51             0.10947113
## 805           6-3 6-2 6-4  1.14  9.55  1.08 7.75             0.08401234
## 806               6-2 6-4  1.14  7.50  1.11 6.37             0.06664251
## 807               6-4 6-1  1.14 10.50  1.08 7.98             0.07056557
## 808           3-6 6-1 6-2  1.13  8.50  1.09 7.31             0.10514533
## 809           6-1 6-0 7-5  1.12  8.15  1.10 6.99             0.08538932
## 810               6-2 6-2  1.11 10.00  1.07 8.33             0.06524706
## 811               7-6 6-2  1.11 10.40  1.08 7.78             0.07006136
## 812               6-1 6-2  1.11  8.25  1.10 6.91             0.07212009
## 813           6-3 6-3 6-4  1.09  9.78  1.07 8.51             0.06876956
##     best_loser_exp_payout avg_winner_exp_payout avg_loser_exp_payout
## 1           -0.0506825632           0.379476882         -0.050682563
## 2           -0.0790095548           1.007370189         -0.088038873
## 3           -0.0710097187           0.854099956         -0.080117467
## 4           -0.1388764824           0.696023025         -0.154533274
## 5           -0.1356263670           0.681087046         -0.151633286
## 6           -0.0081349368          -0.016332043         -0.060338361
## 7           -0.0040265583          -0.165035491         -0.030704418
## 8           -0.1544894692           0.846007643         -0.170003424
## 9           -0.2508843387           1.594465786         -0.277879498
## 10          -0.0919654273           0.381560374         -0.116287782
## 11          -0.1337128817           0.609383264         -0.149321659
## 12          -0.4331644846           2.372212020         -0.452880503
## 13          -0.1081471492           0.446289964         -0.132036065
## 14          -0.2310127534           1.093913566         -0.257760136
## 15          -0.0040956726          -0.113844559         -0.046295009
## 16          -0.0851140608           0.222593116         -0.108980651
## 17          -0.1060156193           0.268946983         -0.121563174
## 18          -0.0259914091          -0.071071432         -0.051400329
## 19          -0.0542274580           0.090473706         -0.078478036
## 20          -0.1592822893           0.626710797         -0.195210397
## 21          -0.1169340322           0.444395446         -0.154037644
## 22          -0.0195345466          -0.096066008         -0.044674686
## 23          -0.1329450207           0.422106278         -0.148024238
## 24          -0.0398166493           0.027214648         -0.079824289
## 25          -0.0225224607          -0.078351175         -0.055657293
## 26          -0.1714994973           0.582749980         -0.198887944
## 27          -0.2947227132           1.130614510         -0.323627520
## 28          -0.0001507249           0.038625810         -0.064141079
## 29          -0.1201686458           0.342326492         -0.142349268
## 30          -0.2410238448           0.802181473         -0.253997796
## 31          -0.1404519634           0.438409545         -0.169103565
## 32          -0.5904019764           2.346035034         -0.604055244
## 33          -0.1975098432           0.623165193         -0.217572097
## 34          -0.1189414798           0.297028684         -0.140967943
## 35          -0.1934618904           0.603012083         -0.219905763
## 36          -0.2843756100           0.984428630         -0.313704478
## 37          -0.0399534165          -0.056183228         -0.063954581
## 38          -0.1216676697           0.383474007         -0.157664896
## 39          -0.3125860418           0.962300114         -0.340082600
## 40          -0.0278117994          -0.039882421         -0.058921822
## 41          -0.1844979112           0.594548062         -0.229803583
## 42          -0.1640730516           0.378885218         -0.177776772
## 43          -0.1025123183           0.205695073         -0.124402262
## 44          -0.0834662842           0.211149544         -0.127459903
## 45          -0.1804186285           0.484083431         -0.206645232
## 46          -0.0665880344           0.061203091         -0.088989922
## 47          -0.0817087060           0.083183715         -0.096762662
## 48          -0.0476602870           0.006000304         -0.077893294
## 49          -0.1502981613           0.337960304         -0.183232341
## 50          -0.0873096840           0.200660021         -0.136454547
## 51          -0.0456517831           0.001858623         -0.075948552
## 52          -0.1604312694           0.458928580         -0.206345184
## 53          -0.2009734852           0.554956577         -0.226542334
## 54          -0.0746886543           0.102347552         -0.104063618
## 55          -0.2457016936           0.677045665         -0.275398477
## 56          -0.2582701254           0.734556239         -0.287472089
## 57          -0.0739358594           0.148258302         -0.110395078
## 58          -0.1173650875           0.239913859         -0.145385243
## 59          -0.0666190814           0.052265947         -0.088667450
## 60          -0.0810253307           0.158107193         -0.117205436
## 61          -0.0992803465           0.185947102         -0.141174284
## 62          -0.0548267878           0.058538046         -0.091461408
## 63          -0.0541382873           0.037750339         -0.083467333
## 64          -0.2873234189           0.729019110         -0.304158299
## 65          -0.0703041334           0.103256843         -0.106338857
## 66          -0.7463842923           2.195496646         -0.754187852
## 67          -0.3603877993           0.935019088         -0.370540374
## 68          -0.1717571753           0.424646169         -0.203859610
## 69          -0.0579503109           0.062731957         -0.094463865
## 70          -0.1593612254           0.387136707         -0.203605371
## 71          -0.1755318255           0.357094671         -0.194558014
## 72          -0.1267500225           0.244140450         -0.153619253
## 73          -0.0950039538           0.128151120         -0.116050373
## 74          -0.1664150095           0.365706928         -0.192262606
## 75          -0.0550208090           0.040484063         -0.091366163
## 76          -0.2325418568           0.539270586         -0.250389721
## 77          -0.0357328124          -0.032901805         -0.065632570
## 78          -0.0878586991           0.120819474         -0.116363115
## 79          -0.2087382629           0.498821190         -0.239171407
## 80          -0.0721849835           0.055670960         -0.093762077
## 81          -0.0438268244          -0.014046356         -0.073475605
## 82          -0.1040942871           0.178255922         -0.137774953
## 83          -0.1321507558           0.229967536         -0.158853809
## 84          -0.1151882881           0.187295914         -0.142624310
## 85          -0.0516182610           0.022397713         -0.080799238
## 86          -0.1097295544           0.203974537         -0.143970725
## 87          -0.2553607540           0.602261440         -0.278450343
## 88          -0.0755807769           0.034291678         -0.089802611
## 89          -0.2408673063           0.534859289         -0.264046931
## 90          -0.3193992732           0.791951378         -0.350103065
## 91          -0.2396976301           0.576895144         -0.279120716
## 92          -0.1119836160           0.176407519         -0.138690876
## 93          -0.2013320747           0.454324977         -0.231133117
## 94          -0.0710203800           0.067377553         -0.105944426
## 95          -0.0263824934          -0.036548100         -0.059054222
## 96          -0.1912794424           0.466965625         -0.233526039
## 97          -0.1316384559           0.248692293         -0.170232302
## 98          -0.1978736573           0.392004922         -0.227582040
## 99          -0.0991761826           0.134585765         -0.125867259
## 100         -0.1168005529           0.146424859         -0.142777007
## 101         -0.2180211880           0.635500150         -0.298915548
## 102         -0.0847201810           0.082319878         -0.105521995
## 103         -0.1111443334           0.147737008         -0.137480798
## 104         -0.1013588579           0.125424990         -0.121628959
## 105         -0.2635884932           0.550002493         -0.280452879
## 106         -0.2862130106           0.615532527         -0.307206746
## 107         -0.1430098211           0.254440074         -0.174286835
## 108         -0.1047091095           0.154938816         -0.137624216
## 109         -0.0646552970           0.053325245         -0.098791965
## 110         -0.0413766857          -0.007627371         -0.076109414
## 111         -0.2109889197           0.438929544         -0.251011221
## 112         -0.1943438899           0.374679511         -0.234916500
## 113         -0.2553974510           0.497768796         -0.277297526
## 114         -0.0593241527          -0.009734071         -0.079922894
## 115         -0.1780008067           0.291282410         -0.207569123
## 116         -0.1037703008           0.209048722         -0.161385067
## 117         -0.0590407144           0.032841607         -0.092646403
## 118         -0.2680481735           0.560884431         -0.294958167
## 119         -0.1734090130           0.327032287         -0.208834341
## 120         -0.1597986104           0.253726953         -0.178469752
## 121         -0.2691339009           0.491126425         -0.290318426
## 122         -0.2853388454           0.615134154         -0.316411069
## 123         -0.0789868601           0.068416549         -0.106075482
## 124         -0.4052635339           0.866423472         -0.431121641
## 125         -0.1882125302           0.348827339         -0.233627214
## 126         -0.0703685294           0.065048742         -0.110209878
## 127         -0.2091605359           0.361908912         -0.231755949
## 128         -0.1460378948           0.216644088         -0.170971095
## 129         -0.1748643671           0.280088314         -0.198609277
## 130         -0.0385852773          -0.006917622         -0.079788765
## 131         -0.6870000922           1.095461196         -0.699194894
## 132         -0.1046277160           0.130798004         -0.137068741
## 133         -0.3175282768           0.634038785         -0.337600975
## 134         -0.0231293772          -0.032604881         -0.057526230
## 135         -0.0880475152           0.064977679         -0.107872569
## 136         -0.1442999940           0.242260979         -0.186781555
## 137         -0.2259569480           0.403932012         -0.259130222
## 138         -0.2555707335           0.433466079         -0.281599729
## 139         -0.0577016447           0.046175188         -0.098085860
## 140         -0.3282868861           0.633584047         -0.361399504
## 141         -0.1595616133           0.272424881         -0.195324949
## 142         -0.0892356509           0.086988261         -0.121532259
## 143         -0.0799364421           0.066765788         -0.112333046
## 144         -0.5486521037           1.134467233         -0.567995585
## 145         -0.0349963455          -0.013106518         -0.075771148
## 146         -0.3028909854           0.556401468         -0.327787736
## 147         -0.2929161337           0.527963436         -0.313263871
## 148         -0.1986396795           0.304179302         -0.221535689
## 149         -0.1537808420           0.237043421         -0.194916496
## 150         -0.0888513924           0.082613660         -0.121161627
## 151         -0.1292406714           0.145428025         -0.154119509
## 152         -0.2257280824           0.393191329         -0.253184533
## 153         -0.1350480771           0.174056491         -0.165081130
## 154         -0.0218347446          -0.033629039         -0.068099317
## 155         -0.0305361580          -0.028985557         -0.077337861
## 156         -0.1310476567           0.170109764         -0.167004305
## 157         -0.6266040227           1.101234058         -0.634329457
## 158         -0.0420771277           0.007675107         -0.088642823
## 159         -0.1937916717           0.304291677         -0.221980774
## 160         -0.0199803000           0.016851826         -0.086197847
## 161         -0.0703983529           0.077507634         -0.115587322
## 162         -0.0387447411          -0.029838997         -0.078248382
## 163         -0.2320031028           0.381339711         -0.264002974
## 164         -0.1677690308           0.242050397         -0.212154682
## 165         -0.1347858180           0.149319392         -0.158987613
## 166         -0.0317387483           0.030392885         -0.097161806
## 167         -0.2051150614           0.326069848         -0.232715233
## 168         -0.0580835313          -0.003353908         -0.084430845
## 169         -0.0864318135           0.097162820         -0.128504033
## 170         -0.0544748906           0.007557395         -0.092806990
## 171         -0.0508413739          -0.021725873         -0.077206891
## 172         -0.4972712246           0.931437297         -0.511432599
## 173         -0.1579906235           0.207691657         -0.202600392
## 174         -0.1144668239           0.157951726         -0.167246947
## 175         -0.2482596637           0.386888160         -0.274181744
## 176         -0.4526745162           0.822543804         -0.471678873
## 177         -0.1409589585           0.198227852         -0.176752335
## 178         -0.2135722005           0.329943193         -0.251021143
## 179         -0.6666139725           1.201011695         -0.684394561
## 180         -0.2775685923           0.403598173         -0.302141089
## 181         -0.4056450981           0.630161177         -0.429419294
## 182          0.0793704135          -0.123718534         -0.007977481
## 183         -0.0403332403           0.005019827         -0.091515468
## 184         -0.2178039851           0.311011152         -0.254064728
## 185         -0.1401047200           0.198611202         -0.191019572
## 186         -0.1407676506           0.201244028         -0.196926628
## 187         -0.0530173219           0.008411149         -0.097807043
## 188         -0.1440716408           0.170266451         -0.178538555
## 189         -0.2429099396           0.362523847         -0.278477929
## 190         -0.0916670453           0.113602808         -0.144408959
## 191         -0.1114868104           0.139011763         -0.153511083
## 192         -0.4890043428           0.839153333         -0.503100775
## 193         -0.3025856773           0.471407075         -0.335131679
## 194         -0.1125500643           0.086303572         -0.130911097
## 195         -0.1831498962           0.234224146         -0.210378233
## 196         -0.1786461864           0.239660367         -0.216976031
## 197         -0.1390343004           0.196777641         -0.193872880
## 198         -0.3799320484           0.637880318         -0.427937309
## 199         -0.2227352641           0.329105209         -0.268757518
## 200         -0.1892969697           0.302340000         -0.255166591
## 201         -0.1721251075           0.197330017         -0.204171878
## 202         -0.1928630616           0.250252310         -0.220131201
## 203         -0.0997725418           0.124009645         -0.161663180
## 204         -0.3978426071           0.592174223         -0.413900138
## 205         -0.0673872923           0.019684818         -0.103488429
## 206         -0.3199847223           0.461084849         -0.346651988
## 207         -0.2492072923           0.354700260         -0.283557285
## 208         -0.4645823104           0.729817610         -0.482429567
## 209         -0.2946508387           0.411384305         -0.326505317
## 210         -0.2112094535           0.281778499         -0.246832252
## 211         -0.4347696168           0.702698434         -0.467589446
## 212         -0.1799072893           0.297705368         -0.252116710
## 213         -0.2380391009           0.319911584         -0.280899401
## 214         -0.2951589315           0.399162366         -0.318043382
## 215         -0.0715070777           0.032414547         -0.107682127
## 216         -0.3516678551           0.488043109         -0.372717600
## 217         -0.2433057285           0.288842881         -0.263088585
## 218         -0.1812804800           0.239373531         -0.222998672
## 219         -0.1706534037           0.197244669         -0.212645636
## 220         -0.1308587594           0.121874967         -0.153730897
## 221         -0.2314963723           0.351232437         -0.271161076
## 222         -0.2008298219           0.252149282         -0.227468828
## 223         -0.4064758910           0.613527086         -0.422303201
## 224         -0.1765619924           0.200473987         -0.208643993
## 225         -0.2414363224           0.328206452         -0.279603048
## 226         -0.0527823287           0.003340908         -0.095559901
## 227         -0.0916742097           0.089152488         -0.147399718
## 228         -0.1164534695           0.093078773         -0.150219579
## 229         -0.1022065471           0.145476500         -0.179317641
## 230         -0.0052501892          -0.027388595         -0.066654498
## 231         -0.1374513679           0.181780941         -0.195660171
## 232         -0.3258897659           0.464870938         -0.367759967
## 233         -0.2623424722           0.367798458         -0.299930117
## 234         -0.1383674085           0.177576954         -0.198354488
## 235         -0.1033444223           0.084085894         -0.169574664
## 236         -0.0898704493           0.051147438         -0.125330042
## 237         -0.0912795540           0.043717234         -0.114580078
## 238         -0.1464803813           0.152379089         -0.183821865
## 239         -0.3618174311           0.495656004         -0.390271431
## 240         -0.0404571231          -0.017271884         -0.086423249
## 241         -0.1843383094           0.225528608         -0.214925623
## 242         -0.0387442699          -0.028898329         -0.080537997
## 243         -0.3410902283           0.473993108         -0.370468371
## 244         -0.3261222193           0.465905414         -0.376039092
## 245         -0.3258590895           0.372117023         -0.354459007
## 246         -0.2183099446           0.259036942         -0.243525753
## 247         -0.0791633767           0.017160450         -0.108489384
## 248         -0.1668269268           0.246569732         -0.233276313
## 249         -0.0745126542           0.037184146         -0.110108321
## 250         -0.0356854926          -0.036549148         -0.070331523
## 251         -0.1692315300           0.206081241         -0.223952806
## 252         -0.0670639009           0.038725364         -0.113420974
## 253         -0.0606312299           0.067509102         -0.133755745
## 254         -0.0819597128           0.025694580         -0.105349274
## 255         -0.0551691194          -0.003917163         -0.090162856
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## 357         -0.1690929205           0.159265487         -0.237269912
## 358         -0.0275800611           0.017455322         -0.122817065
## 359         -0.3427698102           0.341604468         -0.379486581
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## 362         -0.1211474519           0.070425948         -0.164607193
## 363         -0.3996988937           0.334154166         -0.425243622
## 364         -0.1134070421           0.041254515         -0.156077291
## 365         -0.4196306857           0.364437772         -0.450016514
## 366         -0.4174546376           0.411055246         -0.446104409
## 367         -0.1313984590           0.090469591         -0.195065588
## 368         -0.4319628360           0.389541170         -0.450689336
## 369         -0.1303783689           0.075833692         -0.173146646
## 370         -0.2109142362           0.135464966         -0.223710222
## 371         -0.4784427416           0.451441948         -0.501243059
## 372         -0.3036448947           0.251231070         -0.333595652
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## 374         -0.1116645732           0.066196897         -0.179649427
## 375         -0.2862284865           0.246780447         -0.320952506
## 376         -0.2129296340           0.154858683         -0.246965109
## 377         -0.0832928680           0.024495785         -0.136087520
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## 379         -0.2195701023           0.175567898         -0.275600967
## 380         -0.2554477750           0.191935599         -0.294634734
## 381         -0.0958009678           0.021091598         -0.138185297
## 382         -0.1769219477           0.127934040         -0.228905825
## 383         -0.0881157005           0.024576644         -0.137141738
## 384         -0.4006771999           0.358656884         -0.451619638
## 385         -0.1335439427           0.068607203         -0.171012313
## 386         -0.3012447961           0.254809874         -0.344025727
## 387         -0.0953354547           0.042768780         -0.148551016
## 388         -0.1634254736           0.086090770         -0.186408290
## 389         -0.3549818258           0.301543947         -0.391935992
## 390         -0.2649344869           0.209620622         -0.307047615
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## 399         -0.2997818643           0.236963589         -0.339281349
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## 556         -0.4573506173           0.244874993         -0.492080178
## 557         -0.3059322547           0.144396221         -0.346419540
## 558         -0.1543035753           0.045519860         -0.205045361
## 559         -0.2154615353           0.085864649         -0.284333233
## 560         -0.1979269945           0.067337673         -0.240660392
## 561         -0.2930371822           0.141960293         -0.348485246
## 562         -0.2813550502           0.127540168         -0.329264713
## 563         -0.2790155370           0.117221757         -0.322274605
## 564         -0.1202748925           0.024013732         -0.180096200
## 565         -0.1457083165           0.063872474         -0.232749356
## 566         -0.3075159927           0.137172996         -0.355457193
## 567         -0.5356620934           0.288654175         -0.562195688
## 568         -0.1128455182           0.017270199         -0.171989150
## 569         -0.1342323671           0.032744987         -0.199250490
## 570         -0.3183260597           0.158373813         -0.381249808
## 571         -0.2130820825           0.085505439         -0.271715182
## 572         -0.1365065896           0.041903954         -0.192965774
## 573         -0.3077921754           0.145185167         -0.374449225
## 574         -0.2513639217           0.112118520         -0.310689800
## 575         -0.2354957752           0.109952230         -0.313388659
## 576         -0.0934508992           0.005518672         -0.169271369
## 577         -0.1143038279           0.006160999         -0.161631104
## 578         -0.2085345235           0.059291405         -0.243359004
## 579         -0.2579803438           0.103851042         -0.308958793
## 580         -0.1338192026           0.039164215         -0.217229205
## 581         -0.6284394546           0.334300058         -0.668796218
## 582         -0.2968250755           0.153253792         -0.382210602
## 583         -0.1677034834           0.040646974         -0.210982902
## 584         -0.2813707466           0.111938115         -0.325089637
## 585         -0.1871642487           0.049110958         -0.228602934
## 586         -0.1292798561           0.029816808         -0.193777644
## 587         -0.2034019757           0.065793358         -0.240888942
## 588         -0.3401755798           0.141534672         -0.380014035
## 589         -0.2774711460           0.112040602         -0.330271331
## 590         -0.1622135259           0.043772627         -0.207325105
## 591         -0.1370861400           0.044642883         -0.226459361
## 592         -0.1511974780           0.042155617         -0.214071739
## 593         -0.4605305870           0.205743957         -0.501726433
## 594         -0.1641684457           0.048709697         -0.234352775
## 595         -0.1480798277           0.026711015         -0.201719246
## 596         -0.2149215301           0.093210888         -0.297711623
## 597         -0.2912342406           0.113616186         -0.335860233
## 598         -0.2567103714           0.107664148         -0.327241504
## 599         -0.2818254911           0.103349140         -0.317460104
## 600         -0.2491732214           0.086559514         -0.296283921
## 601         -0.2640411746           0.105891699         -0.314889239
## 602         -0.1435088604           0.042850764         -0.213556463
## 603         -0.3034646506           0.120477837         -0.350776486
## 604         -0.4034639991           0.174808992         -0.456348396
## 605         -0.1975460546           0.038808914         -0.227827336
## 606         -0.4751509154           0.206657559         -0.509380204
## 607         -0.2992930991           0.128600583         -0.358717006
## 608         -0.1042593790           0.028557568         -0.211119664
## 609         -0.3608901880           0.153908457         -0.395303793
## 610         -0.3536904526           0.148545401         -0.396777756
## 611         -0.2788324436           0.106635878         -0.339148276
## 612         -0.1025155345           0.015821248         -0.187700501
## 613         -0.1808133383           0.067213191         -0.258263714
## 614         -0.2855210848           0.102882333         -0.329688872
## 615         -0.2197046821           0.067531889         -0.279938005
## 616         -0.4464870412           0.208392705         -0.491588097
## 617         -0.2471131338           0.073331182         -0.285581806
## 618         -0.1504487464           0.022786962         -0.190609351
## 619         -0.4614266998           0.204268540         -0.489772663
## 620         -0.3275173989           0.148241917         -0.405973702
## 621         -0.1742241959           0.025351490         -0.216571673
## 622         -0.5789506045           0.257445320         -0.606018066
## 623         -0.1943378024           0.042075868         -0.233418431
## 624         -0.2613298773           0.065759215         -0.307178368
## 625         -0.3660227940           0.168653028         -0.425665249
## 626         -0.4159403289           0.157793558         -0.439302716
## 627         -0.3314321086           0.133194953         -0.401347705
## 628         -0.1358511889           0.031965947         -0.219286246
## 629         -0.1118327669           0.043523143         -0.244395040
## 630         -0.5131556258           0.199432341         -0.575877907
## 631         -0.2154300821           0.064905754         -0.275342694
## 632         -0.1329456270           0.024786188         -0.230160814
## 633         -0.6409799615           0.269243383         -0.665911909
## 634         -0.7956806396           0.363772172         -0.822044428
## 635         -0.3882234208           0.175143747         -0.468456415
## 636         -0.4403309905           0.171358875         -0.485104511
## 637         -0.1064872936           0.044105139         -0.241201517
## 638         -0.3351382255           0.117569113         -0.376405508
## 639         -0.2909229057           0.080351640         -0.337379681
## 640         -0.3232921799           0.115180246         -0.384195884
## 641         -0.2009567118           0.043356000         -0.240908876
## 642         -0.2627393314           0.091916274         -0.347343015
## 643         -0.1570276512           0.033863604         -0.245059574
## 644         -0.4972374139           0.199475706         -0.538995104
## 645         -0.2917755880           0.079091978         -0.330187760
## 646         -0.1861051129           0.049949971         -0.257838222
## 647         -0.1562614217           0.021001299         -0.216324168
## 648         -0.3589358690           0.143524466         -0.435062235
## 649         -0.2917217649           0.096592371         -0.353725920
## 650         -0.2779901497           0.083940348         -0.337333425
## 651         -0.2443390233           0.069801601         -0.304791901
## 652         -0.4103151264           0.157984074         -0.474990242
## 653         -0.5395064960           0.210498096         -0.579415933
## 654         -0.2123141808           0.070724774         -0.282934289
## 655         -0.2598306313           0.084103857         -0.322720839
## 656         -0.1010907566           0.042681749         -0.224690778
## 657         -0.0817179788           0.025310854         -0.228643102
## 658         -0.0520074638           0.015307377         -0.205884513
## 659         -0.2675132566           0.071195486         -0.300808109
## 660         -0.4506280207           0.159963930         -0.487252819
## 661         -0.3265331582           0.106327603         -0.404083885
## 662         -0.3074586364           0.101786678         -0.398691630
## 663         -0.1833567504           0.048538916         -0.293843778
## 664         -0.5459647591           0.195715108         -0.591368283
## 665         -0.2124839399           0.058608340         -0.284755983
## 666         -0.4943676259           0.179274548         -0.540185446
## 667         -0.3870296923           0.119723377         -0.445497629
## 668         -0.0310905897           0.021018060         -0.222217925
## 669         -0.3195502975           0.091070588         -0.378173656
## 670         -0.1624248315           0.028488696         -0.239701112
## 671         -0.1976769848           0.046245836         -0.257012770
## 672         -0.1720782329           0.044946616         -0.278906848
## 673         -0.1608477132           0.031870990         -0.239826752
## 674         -0.4262991010           0.138150374         -0.488915423
## 675         -0.1952243018           0.040425556         -0.263127251
## 676         -0.3470921427           0.093053235         -0.390757955
## 677         -0.2189857762           0.041501668         -0.267639121
## 678         -0.0640070259           0.011246453         -0.199918334
## 679         -0.1967072560           0.030940322         -0.266874393
## 680         -0.1581844728           0.028153879         -0.255786273
## 681         -0.4408312851           0.125918263         -0.482369533
## 682         -0.3587390740           0.087665985         -0.391773728
## 683         -0.3282262629           0.091290505         -0.401331052
## 684         -0.5398845954           0.170376682         -0.580318979
## 685         -0.1569891418           0.017247271         -0.243698830
## 686         -0.2424284663           0.053558965         -0.308304252
## 687         -0.2393566915           0.034040472         -0.272122865
## 688         -0.4652057387           0.136209171         -0.493179592
## 689         -0.3266065601           0.090642624         -0.391965335
## 690         -0.2623164092           0.064926564         -0.329575795
## 691         -0.2021138694           0.030096401         -0.273807985
## 692         -0.3029384815           0.079525543         -0.370994784
## 693         -0.4489732722           0.139589309         -0.507317279
## 694         -0.4448303617           0.130439022         -0.509350076
## 695         -0.6054507954           0.185861244         -0.629606869
## 696         -0.4387766481           0.124508475         -0.482204646
## 697         -0.6347208286           0.196037032         -0.658356540
## 698         -0.2800430358           0.072302314         -0.356152772
## 699         -0.2522590027           0.034073040         -0.290172631
## 700         -0.3533769641           0.089413130         -0.385210714
## 701         -0.0690237788           0.027739000         -0.238509193
## 702         -0.2964920039           0.075050236         -0.384670118
## 703         -0.1814156660           0.031858314         -0.273097111
## 704         -0.3583014409           0.086154548         -0.405970477
## 705         -0.4756345445           0.136922049         -0.515037729
## 706         -0.3508427020           0.084155653         -0.392846998
## 707         -0.2304758339           0.047596159         -0.292497185
## 708         -0.2964743103           0.070673853         -0.342356421
## 709         -0.1961666706           0.044907113         -0.294770226
## 710         -0.2607926149           0.048280629         -0.322726207
## 711         -0.3268968344           0.079236076         -0.387231012
## 712         -0.2144726513           0.051399634         -0.308735933
## 713         -0.3967270589           0.110177257         -0.462839162
## 714         -0.6081404588           0.181093374         -0.638369623
## 715         -0.7443689279           0.233412123         -0.763250768
## 716         -0.4709174181           0.123270702         -0.512647875
## 717         -0.4985726942           0.134077516         -0.535193790
## 718         -0.3617272502           0.092821480         -0.428041302
## 719         -0.4074727861           0.099680022         -0.450869145
## 720         -0.3575929662           0.090816950         -0.421833670
## 721         -0.2746287518           0.049661278         -0.326299033
## 722         -0.2772722313           0.070208667         -0.367124873
## 723         -0.2553801536           0.074275451         -0.372657779
## 724         -0.3860447795           0.089962688         -0.432899257
## 725         -0.1959829655           0.012690440         -0.258633644
## 726         -0.1201722918           0.037062984         -0.296137833
## 727         -0.6441043167           0.173933409         -0.668347892
## 728         -0.3778949614           0.097815862         -0.443215990
## 729         -0.2571027779           0.043828544         -0.337895314
## 730         -0.5570897349           0.152363245         -0.597973759
## 731         -0.5196426207           0.130034769         -0.574707979
## 732         -0.2928166117           0.062957270         -0.353162927
## 733         -0.5468877736           0.144235718         -0.599995690
## 734         -0.6293283811           0.174184568         -0.666105200
## 735         -0.2866740553           0.071008443         -0.361472940
## 736         -0.1247625365           0.009550147         -0.272879646
## 737         -0.5038855433           0.106779891         -0.563465109
## 738         -0.5178786336           0.116926466         -0.552832433
## 739         -0.1117770489           0.021019276         -0.269593427
## 740         -0.3845626945           0.093796779         -0.446423661
## 741         -0.2890190407           0.042117449         -0.335136725
## 742         -0.2731710954           0.050220784         -0.366620526
## 743         -0.3037905850           0.061194660         -0.362573438
## 744         -0.2794149286           0.035347938         -0.323758625
## 745         -0.3878482584           0.073281830         -0.457121781
## 746         -0.6330564279           0.146925963         -0.671812266
## 747         -0.3657320732           0.066070818         -0.409087096
## 748         -0.4332566038           0.102538723         -0.481211814
## 749         -0.3011869650           0.064332350         -0.403679543
## 750         -0.2971972446           0.041138590         -0.340446645
## 751         -0.4585564851           0.104305238         -0.523790644
## 752         -0.4956075566           0.106706692         -0.556363919
## 753         -0.3142095699           0.060131603         -0.377004838
## 754         -0.3083253245           0.059848030         -0.436976814
## 755         -0.2829663912           0.059409799         -0.423044524
## 756         -0.3677287875           0.067473668         -0.426137214
## 757         -0.7392356689           0.146895032         -0.778871847
## 758         -0.4776749349           0.093306419         -0.526573452
## 759         -0.4539634828           0.087489132         -0.500766613
## 760         -0.5448108216           0.121797984         -0.587587636
## 761         -0.7749500235           0.188845115         -0.809685998
## 762         -0.2335203304           0.028729888         -0.325568697
## 763         -0.2736102195           0.031453460         -0.346249198
## 764         -0.3051899750           0.040563789         -0.371132593
## 765         -0.4550326576           0.091946826         -0.501816397
## 766         -0.2980297909           0.038977133         -0.383446520
## 767         -0.2578933070           0.039953848         -0.349850006
## 768         -0.3118030973           0.046053600         -0.388443207
## 769         -0.5035400895           0.085885022         -0.574316399
## 770         -0.2933679935           0.040397698         -0.378752694
## 771         -0.2839775353           0.019586653         -0.345555467
## 772         -0.3136401419           0.036980119         -0.380846211
## 773         -0.3919659850           0.062838666         -0.473123068
## 774         -0.3322029327           0.031293372         -0.384220810
## 775         -0.3506819827           0.047219290         -0.419433302
## 776         -0.4350459957           0.060712449         -0.500232996
## 777         -0.5299696184           0.080957884         -0.602992196
## 778         -0.4143612065           0.045418657         -0.472925086
## 779         -0.4368160964           0.050195424         -0.502350223
## 780         -0.4478756453           0.061544229         -0.513126705
## 781         -0.4587164210           0.070717137         -0.536901827
## 782         -0.3401123665           0.032130619         -0.442630624
## 783         -0.6906584730           0.122579411         -0.735983239
## 784         -0.3047662988           0.018015653         -0.386774499
## 785         -0.3758335657           0.046087929         -0.457542626
## 786         -0.4739995302           0.061323030         -0.530320804
## 787         -0.8150697947           0.130660302         -0.833899052
## 788         -0.8499951111           0.129843038         -0.865333566
## 789         -0.3196440356           0.030799711         -0.461860379
## 790         -0.3992991793           0.043864508         -0.483397294
## 791         -0.3617217284           0.040124247         -0.449415613
## 792         -0.3904547840           0.031441373         -0.450301042
## 793         -0.6364213561           0.097034818         -0.688182981
## 794         -0.3892870823           0.041136412         -0.477410087
## 795         -0.7908253251           0.116437590         -0.812982068
## 796         -0.4422693965           0.045878215         -0.530093858
## 797         -0.7542038050           0.087269277         -0.784077496
## 798         -0.4772408911           0.056359350         -0.571695808
## 799         -0.6625471083           0.076831478         -0.695793699
## 800         -0.3461407169           0.024289978         -0.535415773
## 801         -0.4866215269           0.046753645         -0.573601574
## 802         -0.5318691558           0.051631429         -0.599141292
## 803         -0.3678377436           0.021094314         -0.554325609
## 804         -0.7039630006           0.070880825         -0.770571325
## 805         -0.5309805713           0.026959059         -0.619382139
## 806         -0.5173849358           0.038572970         -0.590098939
## 807         -0.3604723212           0.014220010         -0.513958964
## 808         -0.8130400713           0.066025139         -0.839214461
## 809         -0.7481455123           0.066007370         -0.783992286
## 810         -0.5968203670           0.026859779         -0.664151366
## 811         -0.6258001039           0.041140780         -0.720069693
## 812         -0.7184601654           0.062461355         -0.764189060
## 813         -0.8095103624           0.049159109         -0.834246747
##     max_exp_payout avg_exp_payout best_odds_profit full_name_winner_winner
## 1       2.66498649    0.379476882            60.00       Sergiy Stakhovsky
## 2       3.46513678    1.007370189            45.00            Steve Darcis
## 3       2.54670227    0.854099956            38.75             Sam Querrey
## 4       1.28018460    0.696023025             9.50            Ivo Karlovic
## 5       1.09636746    0.681087046             9.50             Robin Haase
## 6       0.31892071   -0.016332043             9.15               Dudi Sela
## 7       0.10184309   -0.030704418             8.95           Stan Wawrinka
## 8       1.21386336    0.846007643             8.87            Benoit Paire
## 9       2.08864975    1.594465786             8.50           Jurgen Melzer
## 10      0.70329361    0.381560374             8.00          Radek Stepanek
## 11      0.92774694    0.609383264             7.78            David Ferrer
## 12      3.31034619    2.372212020             7.50            David Ferrer
## 13      0.72128876    0.446289964             7.45            Marsel Ilhan
## 14      1.48486578    1.093913566             6.50            David Ferrer
## 15      0.17009961   -0.046295009             6.50          Simone Bolelli
## 16      0.45975165    0.222593116             6.14            Gilles Simon
## 17      0.57839195    0.268946983             6.09       Fernando Verdasco
## 18      0.07125206   -0.051400329             6.00          Carlos Berlocq
## 19      0.32620001    0.090473706             5.92      Jo-Wilfried Tsonga
## 20      0.91377741    0.626710797             5.80           Ryan Harrison
## 21      0.74101237    0.444395446             5.75           Martin Klizan
## 22      0.07726900   -0.044674686             5.65       Marinko Matosevic
## 23      0.59925446    0.422106278             5.50       Ricardas Berankis
## 24      0.29700838    0.027214648             5.49                Go Soeda
## 25      0.07268252   -0.055657293             5.25              Rajeev Ram
## 26      0.92326193    0.582749980             5.10             Lukas Rosol
## 27      1.51876606    1.130614510             4.97              Rajeev Ram
## 28      0.19271866    0.038625810             4.96           Stan Wawrinka
## 29      0.51435280    0.342326492             4.81         Alejandro Falla
## 30      1.04106713    0.802181473             4.81          Viktor Troicki
## 31      0.63416942    0.438409545             4.76            Donald Young
## 32      2.78734280    2.346035034             4.75              Mardy Fish
## 33      0.88154659    0.623165193             4.68              Ivan Dodig
## 34      0.49636711    0.297028684             4.63       Marcel Granollers
## 35      0.89785786    0.603012083             4.60         Feliciano Lopez
## 36      1.29036138    0.984428630             4.54              Tommy Haas
## 37      0.09978649   -0.056183228             4.50          Simone Bolelli
## 38      0.54030507    0.383474007             4.50       Mikhail Kukushkin
## 39      1.39886688    0.962300114             4.33             Lukas Rosol
## 40      0.17792203   -0.039882421             4.30     Teymuraz Gabashvili
## 41      0.85207463    0.594548062             4.25          Kevin Anderson
## 42      0.64647710    0.378885218             4.23        Thiemo De Bakker
## 43      0.36519285    0.205695073             4.05            Benoit Paire
## 44      0.33386514    0.211149544             4.00          Carlos Berlocq
## 45      0.72167451    0.484083431             4.00            David Ferrer
## 46      0.26635214    0.061203091             4.00            Gael Monfils
## 47      0.23651109    0.083183715             4.00     Alexandr Dolgopolov
## 48      0.20866541    0.006000304             3.95        Santiago Giraldo
## 49      0.62807925    0.337960304             3.77            Dustin Brown
## 50      0.42112861    0.200660021             3.77           Jurgen Melzer
## 51      0.15225871    0.001858623             3.75             Robin Haase
## 52      0.61720857    0.458928580             3.70            Aljaz Bedene
## 53      0.67762137    0.554956577             3.65           Nicolas Mahut
## 54      0.23516051    0.102347552             3.65         Benjamin Becker
## 55      0.88007783    0.677045665             3.63            Benoit Paire
## 56      0.91341935    0.734556239             3.60           Roger Federer
## 57      0.24575193    0.148258302             3.60            Gilles Simon
## 58      0.36869718    0.239913859             3.57            Ivo Karlovic
## 59      0.20599750    0.052265947             3.55         Michael Russell
## 60      0.24379054    0.158107193             3.50            Albert Ramos
## 61      0.35795470    0.185947102             3.50       Marinko Matosevic
## 62      0.19753799    0.058538046             3.48       Marinko Matosevic
## 63      0.18714370    0.037750339             3.45     Alexandr Dolgopolov
## 64      0.94843778    0.729019110             3.44          Jerzy Janowicz
## 65      0.22335822    0.103256843             3.38        Julien Benneteau
## 66      2.50941193    2.195496646             3.36             Andy Murray
## 67      1.13689131    0.935019088             3.34         Mikhail Youzhny
## 68      0.54992912    0.424646169             3.33           Andreas Seppi
## 69      0.16792624    0.062731957             3.33            Aljaz Bedene
## 70      0.58214532    0.387136707             3.30            Gilles Simon
## 71      0.57291296    0.357094671             3.30       Marcel Granollers
## 72      0.41155777    0.244140450             3.30         Feliciano Lopez
## 73      0.28334651    0.128151120             3.30       Ricardas Berankis
## 74      0.52138337    0.365706928             3.30             Juan Monaco
## 75      0.17429960    0.040484063             3.30            Marsel Ilhan
## 76      0.74180619    0.539270586             3.30            Benoit Paire
## 77      0.07567580   -0.032901805             3.26          Viktor Troicki
## 78      0.22140584    0.120819474             3.25          Simone Bolelli
## 79      0.65535604    0.498821190             3.23         Mikhail Youzhny
## 80      0.18482219    0.055670960             3.22            Marc Gicquel
## 81      0.09205364   -0.014046356             3.22           Martin Klizan
## 82      0.37082406    0.178255922             3.20             Lukas Lacko
## 83      0.39617936    0.229967536             3.20           Gilles Muller
## 84      0.31921768    0.187295914             3.20             Tatsuma Ito
## 85      0.12247368    0.022397713             3.15       Federico Delbonis
## 86      0.30798281    0.203974537             3.15          Jerzy Janowicz
## 87      0.74599993    0.602261440             3.13          Ernests Gulbis
## 88      0.17296766    0.034291678             3.06            Lukasz Kubot
## 89      0.68624267    0.534859289             3.01        Julien Benneteau
## 90      0.95308052    0.791951378             3.00            Lukasz Kubot
## 91      0.74725224    0.576895144             3.00           Martin Klizan
## 92      0.32927403    0.176407519             3.00             Lukas Rosol
## 93      0.61591664    0.454324977             3.00           Roger Federer
## 94      0.20607633    0.067377553             3.00     Teymuraz Gabashvili
## 95      0.38626173   -0.036548100             3.00             Andy Murray
## 96      0.58590878    0.466965625             3.00       Fernando Verdasco
## 97      0.41637383    0.248692293             2.97                Go Soeda
## 98      0.60303774    0.392004922             2.95          Carlos Berlocq
## 99      0.30427455    0.134585765             2.92            Ivo Karlovic
## 100     0.36729570    0.146424859             2.90            Malek Jaziri
## 101     0.79674664    0.635500150             2.90      Jo-Wilfried Tsonga
## 102     0.18043386    0.082319878             2.85        Julien Benneteau
## 103     0.31511532    0.147737008             2.85        Marcos Baghdatis
## 104     0.24218378    0.125424990             2.83            Gilles Simon
## 105     0.66384448    0.550002493             2.80           Nicolas Mahut
## 106     0.79134048    0.615532527             2.77          Vasek Pospisil
## 107     0.40422396    0.254440074             2.75           Roger Federer
## 108     0.28136703    0.154938816             2.75       Mikhail Kukushkin
## 109     0.17705924    0.053325245             2.71           Pablo Andujar
## 110     0.12977807   -0.007627371             2.70           Paolo Lorenzi
## 111     0.58453551    0.438929544             2.70            Gilles Simon
## 112     0.53442820    0.374679511             2.65      Matthias Bachinger
## 113     0.65161816    0.497768796             2.65           Gilles Muller
## 114     0.14381982   -0.009734071             2.65            Benoit Paire
## 115     0.48742657    0.291282410             2.64          Victor Hanescu
## 116     0.29540934    0.209048722             2.60          Leonardo Mayer
## 117     0.18039041    0.032841607             2.60            Tobias Kamke
## 118     0.66248046    0.560884431             2.60        Julien Benneteau
## 119     0.47448032    0.327032287             2.60           Roger Federer
## 120     0.35946296    0.253726953             2.60         Benjamin Becker
## 121     0.68868892    0.491126425             2.59        Julien Benneteau
## 122     0.71638137    0.615134154             2.56       Sergiy Stakhovsky
## 123     0.14911266    0.068416549             2.56         Feliciano Lopez
## 124     1.02006199    0.866423472             2.55         Mikhail Youzhny
## 125     0.51310759    0.348827339             2.50       Ricardas Berankis
## 126     0.17592132    0.065048742             2.50          Simone Bolelli
## 127     0.52290134    0.361908912             2.50              John Isner
## 128     0.31834499    0.216644088             2.50           Florian Mayer
## 129     0.42232035    0.280088314             2.50         Thomaz Bellucci
## 130     0.09646319   -0.006917622             2.50        Santiago Giraldo
## 131     1.78863657    1.095461196             2.50           Jurgen Melzer
## 132     0.22912827    0.130798004             2.50           Gilles Muller
## 133     0.74363895    0.634038785             2.50            Marsel Ilhan
## 134     0.09222030   -0.032604881             2.50      Jo-Wilfried Tsonga
## 135     0.17011879    0.064977679             2.45        Santiago Giraldo
## 136     0.35626594    0.242260979             2.45          Kevin Anderson
## 137     0.53359452    0.403932012             2.43       Marcel Granollers
## 138     0.63002832    0.433466079             2.40       Fernando Verdasco
## 139     0.11156114    0.046175188             2.40     Alexandr Dolgopolov
## 140     0.79167283    0.633584047             2.40         Jarkko Nieminen
## 141     0.37341098    0.272424881             2.40             Juan Monaco
## 142     0.20383065    0.086988261             2.40           Steve Johnson
## 143     0.19351024    0.066765788             2.39           Andreas Seppi
## 144     1.26998896    1.134467233             2.35     Alexandr Dolgopolov
## 145     0.07340687   -0.013106518             2.35           Bernard Tomic
## 146     0.67187642    0.556401468             2.33          Viktor Troicki
## 147     0.62131168    0.527963436             2.30        Marcos Baghdatis
## 148     0.41107924    0.304179302             2.30           Matthew Ebden
## 149     0.36074776    0.237043421             2.30           Robby Ginepri
## 150     0.16752454    0.082613660             2.30          Kevin Anderson
## 151     0.24749587    0.145428025             2.30                Go Soeda
## 152     0.48787424    0.393191329             2.30           Tommy Robredo
## 153     0.30983173    0.174056491             2.28       Marcel Granollers
## 154     0.11217430   -0.033629039             2.28          Leonardo Mayer
## 155     0.08700593   -0.028985557             2.28            Dustin Brown
## 156     0.31436987    0.170109764             2.28            Benoit Paire
## 157     1.41307798    1.101234058             2.25           Jurgen Melzer
## 158     0.08802130    0.007675107             2.25          Leonardo Mayer
## 159     0.41770834    0.304291677             2.25             Robin Haase
## 160     0.09792971    0.016851826             2.25     Teymuraz Gabashvili
## 161     0.15194073    0.077507634             2.25              Joao Sousa
## 162     0.10338734   -0.029838997             2.23       Marco Chiudinelli
## 163     0.49334023    0.381339711             2.20         Benjamin Becker
## 164     0.42457393    0.242050397             2.20               Pere Riba
## 165     0.26385638    0.149319392             2.20           Jeremy Chardy
## 166     0.10646216    0.030392885             2.20           Pablo Andujar
## 167     0.43358903    0.326069848             2.20      Jo-Wilfried Tsonga
## 168     0.07514904   -0.003353908             2.15            Malek Jaziri
## 169     0.25276046    0.097162820             2.14           Roger Federer
## 170     0.13034217    0.007557395             2.13              Bjorn Phau
## 171     0.06348964   -0.021725873             2.12         Benjamin Becker
## 172     1.01541283    0.931437297             2.12        Marcos Baghdatis
## 173     0.37137148    0.207691657             2.10       Sergiy Stakhovsky
## 174     0.28201798    0.157951726             2.10       Marcel Granollers
## 175     0.49283101    0.386888160             2.10            Malek Jaziri
## 176     0.92172986    0.822543804             2.10          Radek Stepanek
## 177     0.25067554    0.198227852             2.10          Kevin Anderson
## 178     0.43689667    0.329943193             2.09            Malek Jaziri
## 179     1.37211508    1.201011695             2.05            Gilles Simon
## 180     0.55107769    0.403598173             2.05         Albert Montanes
## 181     0.84147837    0.630161177             2.05           Jurgen Melzer
## 182     0.13202026   -0.007977481             2.01             Juan Monaco
## 183     0.08066648    0.005019827             2.00             Lukas Rosol
## 184     0.44596818    0.311011152             2.00         Albert Montanes
## 185     0.30283826    0.198611202             2.00        Adrian Mannarino
## 186     0.31523069    0.201244028             2.00     Alexandr Dolgopolov
## 187     0.08044052    0.008411149             2.00           Martin Klizan
## 188     0.27665431    0.170266451             2.00            Pablo Cuevas
## 189     0.47565760    0.362523847             2.00         Illya Marchenko
## 190     0.24193622    0.113602808             2.00           Denis Istomin
## 191     0.19895975    0.139011763             2.00           Fabio Fognini
## 192     0.94276761    0.839153333             2.00           Jurgen Melzer
## 193     0.60517135    0.471407075             2.00           Denis Istomin
## 194     0.15225772    0.086303572             1.97            Ivo Karlovic
## 195     0.34352813    0.234224146             1.95           Tommy Robredo
## 196     0.33467083    0.239660367             1.95        Julien Benneteau
## 197     0.33226190    0.196777641             1.95             Blaz Kavcic
## 198     0.76987067    0.637880318             1.95        Marcos Baghdatis
## 199     0.44149278    0.329105209             1.95             Rui Machado
## 200     0.43060076    0.302340000             1.90         Albert Montanes
## 201     0.35107278    0.197330017             1.90             Robin Haase
## 202     0.31844789    0.250252310             1.90           Gilles Muller
## 203     0.26833773    0.124009645             1.90             Marin Cilic
## 204     0.73582904    0.592174223             1.90          Ernests Gulbis
## 205     0.14714542    0.019684818             1.88         Stephane Robert
## 206     0.59997124    0.461084849             1.88             Sam Querrey
## 207     0.46674314    0.354700260             1.88            David Ferrer
## 208     0.84556749    0.729817610             1.87       Nikolay Davydenko
## 209     0.55851703    0.411384305             1.86       Fernando Verdasco
## 210     0.39964319    0.281778499             1.85         Feliciano Lopez
## 211     0.81070542    0.702698434             1.85            David Ferrer
## 212     0.38002250    0.297705368             1.85       Ricardas Berankis
## 213     0.46656843    0.319911584             1.80          Kevin Anderson
## 214     0.51847078    0.399162366             1.80              Tommy Haas
## 215     0.11183105    0.032414547             1.80            Benoit Paire
## 216     0.62121428    0.488043109             1.80               Dudi Sela
## 217     0.41520003    0.288842881             1.80           Denis Istomin
## 218     0.33986328    0.239373531             1.80           Andreas Seppi
## 219     0.33027185    0.197244669             1.80           Gilles Muller
## 220     0.19895035    0.121874967             1.80           Jeremy Chardy
## 221     0.41173538    0.351232437             1.80         Richard Gasquet
## 222     0.30821567    0.252149282             1.80            Benoit Paire
## 223     0.69208833    0.613527086             1.80         Benjamin Becker
## 224     0.29353399    0.200473987             1.78             Robin Haase
## 225     0.45370627    0.328206452             1.78           Andreas Seppi
## 226     0.07723036    0.003340908             1.77          Jerzy Janowicz
## 227     0.21754851    0.089152488             1.75       Alex Bogomolov Jr
## 228     0.20238665    0.093078773             1.75           Andreas Seppi
## 229     0.23531779    0.145476500             1.75         Alejandro Falla
## 230     0.06138149   -0.027388595             1.75              John Isner
## 231     0.29477992    0.181780941             1.75        Julien Benneteau
## 232     0.59856948    0.464870938             1.75         Mikhail Youzhny
## 233     0.45792471    0.367798458             1.75            Milos Raonic
## 234     0.25032302    0.177576954             1.75       Ricardas Berankis
## 235     0.34897566    0.084085894             1.75           Martin Klizan
## 236     0.12476866    0.051147438             1.75             Lukas Rosol
## 237     0.13556435    0.043717234             1.72             Juan Monaco
## 238     0.26435115    0.152379089             1.71       Fernando Verdasco
## 239     0.60842372    0.495656004             1.71         Alejandro Falla
## 240     0.14864325   -0.017271884             1.70            Ivo Karlovic
## 241     0.32357090    0.225528608             1.70            Rafael Nadal
## 242     0.08795623   -0.028898329             1.70          Simone Bolelli
## 243     0.56684307    0.473993108             1.70        Julien Benneteau
## 244     0.57687037    0.465905414             1.70         Thomaz Bellucci
## 245     0.59686033    0.372117023             1.70            Dustin Brown
## 246     0.33834636    0.259036942             1.70       Sergiy Stakhovsky
## 247     0.11639562    0.017160450             1.70   Roberto Bautista Agut
## 248     0.31989736    0.246569732             1.70          Ernests Gulbis
## 249     0.08192542    0.037184146             1.66         Jarkko Nieminen
## 250     0.12402599   -0.036549148             1.66         Feliciano Lopez
## 251     0.33171470    0.206081241             1.65     Alexandr Dolgopolov
## 252     0.11442195    0.038725364             1.65        Horacio Zeballos
## 253     0.15938489    0.067509102             1.65             Robin Haase
## 254     0.10044155    0.025694580             1.65           Jurgen Melzer
## 255     0.10444331   -0.003917163             1.65            Malek Jaziri
## 256     0.22412817    0.104025026             1.65           Pablo Andujar
## 257     0.12857883    0.039144285             1.65           Martin Klizan
## 258     0.11115758    0.056441482             1.64           Jurgen Melzer
## 259     0.17790078    0.097283999             1.63             Marin Cilic
## 260     0.71229543    0.575572224             1.63          Jerzy Janowicz
## 261     0.13548920    0.070727457             1.63            Gilles Simon
## 262     0.24896358    0.076692742             1.61         Richard Gasquet
## 263     0.23437006    0.101437899             1.60   Philipp Kohlschreiber
## 264     0.29225566    0.182910946             1.60   Philipp Kohlschreiber
## 265     0.69921915    0.555439069             1.60           Andreas Seppi
## 266     0.47700548    0.384692642             1.56         Michael Russell
## 267     0.11699436    0.047182215             1.56             Lukas Rosol
## 268     0.08432603    0.012037625             1.55         Stephane Robert
## 269     0.14239998    0.016959985             1.55            Pablo Cuevas
## 270     0.25324149    0.145118698             1.55         Feliciano Lopez
## 271     0.07784658   -0.006690409             1.55              John Isner
## 272     0.20235503    0.159918973             1.55           Jeremy Chardy
## 273     0.19589041    0.120854151             1.55             Sam Querrey
## 274     0.42655246    0.286694377             1.55          Evgeny Donskoy
## 275     0.10902496    0.038610675             1.52           Steve Johnson
## 276     0.37033899    0.277155939             1.50               Dudi Sela
## 277     0.57565924    0.462211778             1.50          Radek Stepanek
## 278     0.30204618    0.203090671             1.50           Jeremy Chardy
## 279     0.19460527    0.113372108             1.50        Julien Benneteau
## 280     0.52568487    0.434143774             1.50             Juan Monaco
## 281     0.39955039    0.315577370             1.50        Marcos Baghdatis
## 282     0.16550146    0.090909367             1.50          Ernests Gulbis
## 283     0.37530160    0.265277468             1.50            Steve Darcis
## 284     0.15525445    0.072076133             1.50           Mischa Zverev
## 285     0.14466833    0.051982637             1.47          Jerzy Janowicz
## 286     0.17635749    0.118739982             1.45          Ernests Gulbis
## 287     0.70137403    0.597208270             1.45           Nicolas Mahut
## 288     0.13647509    0.006592223             1.45           Nicolas Mahut
## 289     0.30550989    0.230909324             1.45             Jan Hernych
## 290     0.34592086    0.263179824             1.44            Ivo Karlovic
## 291     0.12610646    0.066108984             1.44             Marin Cilic
## 292     0.23813523    0.187183162             1.43             Sam Querrey
## 293     0.37732078    0.320406702             1.42             Andy Murray
## 294     0.14634587    0.017381962             1.40         Dmitry Tursunov
## 295     0.24774650    0.148966572             1.40       Mikhail Kukushkin
## 296     0.06928503    0.006910074             1.40           Denis Istomin
## 297     0.19142516    0.097103998             1.40            Donald Young
## 298     0.15461493    0.082451500             1.40       Sergiy Stakhovsky
## 299     0.12643448   -0.009676349             1.40       Marinko Matosevic
## 300     0.29771229    0.178755326             1.40          Carlos Berlocq
## 301     0.13351721    0.076841352             1.40            Steve Darcis
## 302     0.68333558    0.550071511             1.40       Marcel Granollers
## 303     0.28799023    0.191390964             1.40     Alexandr Dolgopolov
## 304     0.29699800    0.231603145             1.38               Dudi Sela
## 305     0.30825102    0.209307668             1.38               Dudi Sela
## 306     0.32721805    0.226840211             1.38           Igor Sijsling
## 307     0.27590671    0.195492423             1.38            Gael Monfils
## 308     0.65467321    0.557339487             1.38          Vasek Pospisil
## 309     0.37075095    0.255561794             1.38             Robin Haase
## 310     0.58212402    0.361828268             1.37         Thomaz Bellucci
## 311     0.14162331    0.073899896             1.36        Santiago Giraldo
## 312     0.20738515    0.120042393             1.35           Pablo Andujar
## 313     0.30039488    0.178655783             1.35         Benjamin Becker
## 314     0.23269903    0.143525054             1.35            Albert Ramos
## 315     0.30296697    0.208709785             1.35             Marin Cilic
## 316     0.20756433    0.115070043             1.35           Andreas Seppi
## 317     0.07771001   -0.014009989             1.35         Alejandro Falla
## 318     0.47460342    0.374204893             1.35            Gilles Simon
## 319     0.35675979    0.270158103             1.35          Andrey Golubev
## 320     0.79905546    0.668911023             1.35       Marcel Granollers
## 321     0.36990069    0.282460217             1.35           Stan Wawrinka
## 322     0.11766803    0.027303383             1.35            Dustin Brown
## 323     0.14619277    0.082786365             1.35              John Isner
## 324     0.27929475    0.181306219             1.35             Sam Querrey
## 325     0.43519544    0.343195731             1.34        Marcos Baghdatis
## 326     0.08550730   -0.012328126             1.33           Andreas Seppi
## 327     0.42796455    0.329906898             1.33            Benoit Paire
## 328     0.47349132    0.391279355             1.33        Marcos Baghdatis
## 329     0.25019821    0.195841763             1.30              John Isner
## 330     0.25522361    0.217021151             1.30         Albert Montanes
## 331     0.17506511    0.093321453             1.30          Radek Stepanek
## 332     0.20128802    0.070713231             1.30            Ivo Karlovic
## 333     0.16000027    0.074261117             1.30          Victor Hanescu
## 334     0.19776088    0.135269008             1.30             Robin Haase
## 335     0.32025654    0.257113832             1.30        Marcos Baghdatis
## 336     0.11927746    0.050850016             1.29     Teymuraz Gabashvili
## 337     0.15179917    0.086413192             1.29             Sam Querrey
## 338     0.66152007    0.565945904             1.26      Jo-Wilfried Tsonga
## 339     0.36165042    0.295375404             1.26            Gael Monfils
## 340     0.23825260    0.122682357             1.25         Michael Russell
## 341     0.33874212    0.249492646             1.25       Ricardas Berankis
## 342     0.67383115    0.554803161             1.25        Janko Tipsarevic
## 343     0.11267773    0.018718281             1.25             Jiri Vesely
## 344     0.25165345    0.195525491             1.23         Richard Gasquet
## 345     0.13388822    0.052166543             1.22              John Isner
## 346     0.18295796    0.113685645             1.22           Florian Mayer
## 347     0.14372429    0.087053271             1.22            Milos Raonic
## 348     0.31741603    0.222467130             1.22         Mikhail Youzhny
## 349     0.40352311    0.326967305             1.20           Nicolas Mahut
## 350     0.10058046    0.035546164             1.20       Fernando Verdasco
## 351     0.36206282    0.324915647             1.20            Benoit Paire
## 352     0.07715563    0.013505520             1.20               Dudi Sela
## 353     0.22055952    0.159531544             1.20           Tomas Berdych
## 354     0.12799781   -0.005311019             1.20          Viktor Troicki
## 355     0.20086389    0.129903753             1.20           Tomas Berdych
## 356     0.21443907    0.148196940             1.20          Viktor Troicki
## 357     0.26256637    0.159265487             1.20           Nicolas Mahut
## 358     0.09725574    0.017455322             1.20              John Isner
## 359     0.39223105    0.341604468             1.20           Denis Istomin
## 360     0.13954847    0.077391284             1.20        Marcos Baghdatis
## 361     0.15063373    0.082017955             1.18           Denis Istomin
## 362     0.12213735    0.070425948             1.17      Matthias Bachinger
## 363     0.47709925    0.334154166             1.17             Juan Monaco
## 364     0.13591402    0.041254515             1.16            Ivo Karlovic
## 365     0.49670470    0.364437772             1.15             Juan Monaco
## 366     0.46558878    0.411055246             1.15           Jeremy Chardy
## 367     0.17225481    0.090469591             1.15            Tobias Kamke
## 368     0.47896709    0.389541170             1.15          Viktor Troicki
## 369     0.12831338    0.075833692             1.15           Andreas Seppi
## 370     0.23295438    0.135464966             1.15         Nicolas Almagro
## 371     0.53009151    0.451441948             1.14         Mikhail Youzhny
## 372     0.33256109    0.251231070             1.13           Jeremy Chardy
## 373     0.21307878    0.156126729             1.13         Richard Gasquet
## 374     0.16461507    0.066196897             1.13           Andreas Seppi
## 375     0.30819820    0.246780447             1.13           Andreas Seppi
## 376     0.22380547    0.154858683             1.13            Marsel Ilhan
## 377     0.10250308    0.024495785             1.12            Gilles Simon
## 378     0.16047818    0.099979320             1.11        Marcos Baghdatis
## 379     0.26553483    0.175567898             1.11           Florian Mayer
## 380     0.27707386    0.191935599             1.10           Nicolas Mahut
## 381     0.11103231    0.021091598             1.10        Santiago Giraldo
## 382     0.19028215    0.127934040             1.10         Thomaz Bellucci
## 383     0.07045321    0.024576644             1.10           Martin Klizan
## 384     0.47071106    0.358656884             1.10        Marcos Baghdatis
## 385     0.11645529    0.068607203             1.10           Kei Nishikori
## 386     0.35133371    0.254809874             1.10            Gael Monfils
## 387     0.08406655    0.042768780             1.10           Martin Klizan
## 388     0.13472170    0.086090770             1.10           Igor Sijsling
## 389     0.39451137    0.301543947             1.10       Fernando Verdasco
## 390     0.29602210    0.209620622             1.10           Tommy Robredo
## 391     0.30828634    0.177457710             1.10          Viktor Troicki
## 392     0.19381626    0.063064956             1.10               Dudi Sela
## 393     0.39714951    0.297353117             1.10             Juan Monaco
## 394     0.48810602    0.268433231             1.10           Jurgen Melzer
## 395     0.39784207    0.304652597             1.10          Jerzy Janowicz
## 396     0.15850820    0.119891261             1.10            Ivo Karlovic
## 397     0.12121766    0.051808952             1.10         Nicolas Almagro
## 398     0.40445811    0.310379575             1.09         Jarkko Nieminen
## 399     0.33950979    0.236963589             1.09       Ricardas Berankis
## 400     0.12757068    0.051676502             1.08               Dudi Sela
## 401     0.18254534    0.079216132             1.06            Marsel Ilhan
## 402     0.32176034    0.238348276             1.06       Ricardas Berankis
## 403     0.16506403    0.102548396             1.05            Dustin Brown
## 404     0.31520415    0.231800957             1.05           Jurgen Melzer
## 405     0.37301745    0.299343339             1.05              Tommy Haas
## 406     0.08380806    0.020365641             1.05        Santiago Giraldo
## 407     0.29390802    0.237102301             1.05             Marin Cilic
## 408     0.09989514    0.040876372             1.05       Fernando Verdasco
## 409     0.09531459   -0.016888372             1.05             Robin Haase
## 410     0.36460752    0.277647235             1.04              Tommy Haas
## 411     0.12857277    0.056299634             1.03          Ernests Gulbis
## 412     0.20353251    0.132387728             1.03         Jarkko Nieminen
## 413     0.19254393    0.133797928             1.03         Jarkko Nieminen
## 414     0.28813149    0.192478161             1.02           Denis Istomin
## 415     0.36163918    0.300972088             1.02          Lleyton Hewitt
## 416     0.09266542    0.032867807             1.01           Pablo Andujar
## 417     0.15488036    0.091361940             1.00          Victor Hanescu
## 418     0.14693102    0.072380503             1.00             Lukas Rosol
## 419     0.10588607    0.017415185             1.00             Andy Murray
## 420     0.43281063    0.332513887             1.00      Jo-Wilfried Tsonga
## 421     0.11437955    0.053088673             1.00         Albert Montanes
## 422     0.10538633    0.050117012             1.00         Benjamin Becker
## 423     0.29535311    0.185248095             1.00         Albert Montanes
## 424     0.21934972    0.146188737             1.00           Tomas Berdych
## 425     0.13675501    0.085601034             1.00             Sam Querrey
## 426     0.08173468    0.033056624             1.00          Novak Djokovic
## 427     0.10471129    0.032905059             1.00        Marcos Baghdatis
## 428     0.10123093    0.051675542             1.00            Ivo Karlovic
## 429     0.13309619    0.041992978             0.99            Milos Raonic
## 430     0.29043387    0.205278340             0.97           Tommy Robredo
## 431     0.78757079   -0.047233841             0.97           Roger Federer
## 432     0.09998566   -0.028439058             0.97           Gilles Muller
## 433     0.07358953    0.024292054             0.96         Albert Montanes
## 434     0.09235133    0.042192344             0.96         Jarkko Nieminen
## 435     0.27642091    0.210963428             0.95            Ivo Karlovic
## 436     0.10467500    0.042360003             0.95            Albert Ramos
## 437     0.20863103    0.134253740             0.95            Gilles Simon
## 438     0.12950765    0.088961226             0.95             Sam Querrey
## 439     0.44282155    0.383628870             0.95       Fernando Verdasco
## 440     0.40494143    0.332893150             0.95      Jo-Wilfried Tsonga
## 441     0.10216664    0.051297414             0.95            Gael Monfils
## 442     0.25544051    0.197497105             0.95              John Isner
## 443     0.17783454    0.092836173             0.94          Viktor Troicki
## 444     0.41043695    0.345004313             0.94          Viktor Troicki
## 445     0.07911507    0.028793638             0.93           Andreas Seppi
## 446     0.06722731    0.022989908             0.93           Roger Federer
## 447     0.20361938    0.128782941             0.93            Dustin Brown
## 448     0.19222212    0.148755687             0.92         Jarkko Nieminen
## 449     0.15654391    0.102330911             0.92         Jarkko Nieminen
## 450     0.13684402    0.065419262             0.91         Jarkko Nieminen
## 451     0.18897377    0.132948824             0.91   Philipp Kohlschreiber
## 452     0.11050428    0.063991009             0.91           Martin Klizan
## 453     0.17531490    0.101473126             0.91          Viktor Troicki
## 454     0.13794423    0.072408174             0.91            Malek Jaziri
## 455     0.34017645    0.234926991             0.91         Feliciano Lopez
## 456     0.09799620    0.063504171             0.91          Vasek Pospisil
## 457     0.14897658    0.076409634             0.90          Kevin Anderson
## 458     0.22832518    0.182831655             0.89             Sam Querrey
## 459     0.12575192    0.047907370             0.88         Mikhail Youzhny
## 460     0.50434914    0.368317566             0.88       Fernando Verdasco
## 461     0.28215658    0.193496817             0.88          Ernests Gulbis
## 462     0.35758608    0.278152850             0.88            Rafael Nadal
## 463     0.14743905    0.086078673             0.87           Denis Istomin
## 464     0.06916172   -0.028557363             0.86             Lukas Lacko
## 465     0.07134943    0.019509945             0.86   Roberto Bautista Agut
## 466     0.15330899    0.103436173             0.85         Jarkko Nieminen
## 467     0.15653688    0.119027575             0.85         Richard Gasquet
## 468     0.06225428    0.016318956             0.85          Radek Stepanek
## 469     0.20995201    0.124928352             0.85      Jo-Wilfried Tsonga
## 470     0.13446107    0.073138848             0.85         Thomaz Bellucci
## 471     0.20162059    0.143163369             0.85           Igor Sijsling
## 472     0.16435396    0.069946879             0.85           Denis Istomin
## 473     0.21048315    0.151274733             0.84         Mikhail Youzhny
## 474     0.20678834    0.141202014             0.84           Bernard Tomic
## 475     0.38470637    0.294399430             0.84         Nicolas Almagro
## 476     0.22315053    0.163322510             0.84      Jo-Wilfried Tsonga
## 477     0.13077105    0.068980285             0.83           Tommy Robredo
## 478     0.37459362    0.299479217             0.83          Jerzy Janowicz
## 479     0.29622468    0.239559121             0.83             Andy Murray
## 480     0.16139218    0.104274531             0.83           Andreas Seppi
## 481     0.26926229    0.192967840             0.83          Viktor Troicki
## 482     0.14696971    0.090561365             0.83            Gilles Simon
## 483     0.15599286    0.111774550             0.83        Marcos Baghdatis
## 484     0.24500403    0.100556050             0.81       Fernando Verdasco
## 485     0.09528304    0.040821453             0.81   Philipp Kohlschreiber
## 486     0.22829584    0.180528784             0.80              John Isner
## 487     0.18642867    0.113924698             0.80           Jurgen Melzer
## 488     0.16797696    0.103089355             0.80               Dudi Sela
## 489     0.15217065    0.056156431             0.80             Juan Monaco
## 490     0.18488539    0.132223817             0.80         Benjamin Becker
## 491     0.33979199    0.257915816             0.80             Andy Murray
## 492     0.23008257    0.154910856             0.80           Tomas Berdych
## 493     0.19518593    0.088947177             0.80          Viktor Troicki
## 494     0.23822958    0.196955262             0.80               Dudi Sela
## 495     0.15403248    0.115564732             0.80         Richard Gasquet
## 496     0.08554649    0.001115098             0.80         Nicolas Almagro
## 497     0.15542452    0.084815244             0.80             Marin Cilic
## 498     0.13343690    0.013127958             0.79           Tommy Robredo
## 499     0.10427393    0.017906134             0.79         Albert Montanes
## 500     0.29139206    0.233676212             0.79            Rafael Nadal
## 501     0.10059019    0.026393097             0.78         Richard Gasquet
## 502     0.20266215    0.148609920             0.78         Feliciano Lopez
## 503     0.19791970    0.117161069             0.78             Juan Monaco
## 504     0.30605226    0.217506345             0.77        Julien Benneteau
## 505     0.25928774    0.188141540             0.77           Roger Federer
## 506     0.06364945    0.003556259             0.77         Feliciano Lopez
## 507     0.28924982    0.230978644             0.77        Marcos Baghdatis
## 508     0.14238662    0.084299168             0.77             Juan Monaco
## 509     0.24566628    0.133063682             0.77            Ivo Karlovic
## 510     0.28879882    0.237829378             0.77        Marcos Baghdatis
## 511     0.20990418    0.114205546             0.77        Marcos Baghdatis
## 512     0.26136168    0.196860230             0.76            Rafael Nadal
## 513     0.21252090    0.171184962             0.76          Jerzy Janowicz
## 514     0.09480880    0.057485769             0.76          Novak Djokovic
## 515     0.23826273    0.189013640             0.76          Viktor Troicki
## 516     0.09223147    0.036059561             0.75          Leonardo Mayer
## 517     0.27992580    0.228728770             0.75            Rafael Nadal
## 518     0.21310270    0.171510605             0.75             Andy Murray
## 519     0.10601298    0.023852020             0.75             Robin Haase
## 520     0.24541361    0.167130466             0.75          Ernests Gulbis
## 521     0.13407561    0.088712589             0.75            Gilles Simon
## 522     0.07772110    0.046752107             0.74          Novak Djokovic
## 523     0.14669048    0.061018201             0.74         Grigor Dimitrov
## 524     0.14085727    0.101517363             0.74             Andy Murray
## 525     0.40238942    0.321792324             0.74         Mikhail Youzhny
## 526     0.16453644    0.090916320             0.74         Nicolas Almagro
## 527     0.15552089    0.089111641             0.74           Tommy Robredo
## 528     0.17683870    0.108813338             0.73           Tomas Berdych
## 529     0.11896540    0.054285319             0.73             Andy Murray
## 530     0.24302254    0.185541733             0.73          Jerzy Janowicz
## 531     0.09024009    0.039824367             0.73        Santiago Giraldo
## 532     0.30559892    0.252771223             0.73             Andy Murray
## 533     0.18079289    0.132737364             0.72         Benjamin Becker
## 534     0.16888396    0.114199327             0.71         Richard Gasquet
## 535     0.16571590    0.124813585             0.71         Mikhail Youzhny
## 536     0.22223937    0.136468182             0.71   Philipp Kohlschreiber
## 537     0.12388351    0.071304162             0.71           Bernard Tomic
## 538     0.15157524    0.064028580             0.71              Ivan Dodig
## 539     0.13230692    0.032397486             0.70   Philipp Kohlschreiber
## 540     0.18150750    0.132857188             0.70          Carlos Berlocq
## 541     0.21930227    0.169095707             0.70          Kevin Anderson
## 542     0.12470043    0.065157466             0.70            Gael Monfils
## 543     0.07371321    0.042133414             0.70            David Goffin
## 544     0.10859987    0.036866934             0.70         Richard Gasquet
## 545     0.06489687   -0.017018275             0.69         Dmitry Tursunov
## 546     0.18353580    0.127510433             0.69             Juan Monaco
## 547     0.16307552    0.108018686             0.69            Gilles Simon
## 548     0.13580164    0.075315164             0.69          Viktor Troicki
## 549     0.15549547    0.073448457             0.69            David Ferrer
## 550     0.12823083    0.074823450             0.69           Tomas Berdych
## 551     0.06741993    0.029297793             0.68              Ivan Dodig
## 552     0.24169242    0.197346267             0.68       Fernando Verdasco
## 553     0.30625561    0.236277628             0.68         Mikhail Youzhny
## 554     0.16817021    0.077776091             0.68             Lukas Rosol
## 555     0.25613357    0.211271661             0.68             Marin Cilic
## 556     0.30751021    0.244874993             0.67           Roger Federer
## 557     0.18704453    0.144396221             0.67          Viktor Troicki
## 558     0.10507479    0.045519860             0.67            Milos Raonic
## 559     0.16993159    0.085864649             0.67            Ivo Karlovic
## 560     0.12104020    0.067337673             0.67           Martin Klizan
## 561     0.20700866    0.141960293             0.67            David Ferrer
## 562     0.19935801    0.127540168             0.67            Rafael Nadal
## 563     0.18126632    0.117221757             0.66             Robin Haase
## 564     0.07586253    0.024013732             0.66            Ivo Karlovic
## 565     0.12485879    0.063872474             0.66         Jarkko Nieminen
## 566     0.21787560    0.137172996             0.66         Nicolas Almagro
## 567     0.33728263    0.288654175             0.65       Nikolay Davydenko
## 568     0.07595886    0.017270199             0.65            Albert Ramos
## 569     0.08536894    0.032744987             0.65             Sam Querrey
## 570     0.21739923    0.158373813             0.65             Juan Monaco
## 571     0.14081782    0.085505439             0.65             Juan Monaco
## 572     0.10201380    0.041903954             0.65           Stan Wawrinka
## 573     0.22698411    0.145185167             0.65            Rafael Nadal
## 574     0.16951819    0.112118520             0.63         Benjamin Becker
## 575     0.15975778    0.109952230             0.63             Juan Monaco
## 576     0.09266362    0.005518672             0.63             Marin Cilic
## 577     0.07897528    0.006160999             0.63            Ivo Karlovic
## 578     0.11396451    0.059291405             0.63       Ricardas Berankis
## 579     0.16119395    0.103851042             0.62             Marin Cilic
## 580     0.10029152    0.039164215             0.62           Ryan Harrison
## 581     0.39455877    0.334300058             0.62        Marcos Baghdatis
## 582     0.21316308    0.153253792             0.62            David Ferrer
## 583     0.08067186    0.040646974             0.62          Jerzy Janowicz
## 584     0.17734624    0.111938115             0.62           Fabio Fognini
## 585     0.10361023    0.049110958             0.62       Sergiy Stakhovsky
## 586     0.09756791    0.029816808             0.62           Tomas Berdych
## 587     0.10704987    0.065793358             0.61       Fernando Verdasco
## 588     0.20912554    0.141534672             0.61         Richard Gasquet
## 589     0.16258790    0.112040602             0.61            Gilles Simon
## 590     0.09121684    0.043772627             0.61           Stan Wawrinka
## 591     0.10690637    0.044642883             0.60          Michael Llodra
## 592     0.09700591    0.042155617             0.60        Julien Benneteau
## 593     0.28612689    0.205743957             0.60            David Ferrer
## 594     0.08956852    0.048709697             0.60            Dustin Brown
## 595     0.09515842    0.026711015             0.60         Thomaz Bellucci
## 596     0.14322707    0.093210888             0.60         Feliciano Lopez
## 597     0.17261572    0.113616186             0.59           Tomas Berdych
## 598     0.15867500    0.107664148             0.59       Fernando Verdasco
## 599     0.15416127    0.103349140             0.59       Fernando Verdasco
## 600     0.12183742    0.086559514             0.59           Pablo Andujar
## 601     0.15715820    0.105891699             0.58             Andy Murray
## 602     0.07693085    0.042850764             0.58            Gilles Simon
## 603     0.16470723    0.120477837             0.58       Federico Delbonis
## 604     0.23788599    0.174808992             0.57       Nikolay Davydenko
## 605     0.09458389    0.038808914             0.57          Carlos Berlocq
## 606     0.27144454    0.206657559             0.57             Andy Murray
## 607     0.18126861    0.128600583             0.57             Andy Murray
## 608     0.07655692    0.028557568             0.57             Sam Querrey
## 609     0.18407600    0.153908457             0.57   Philipp Kohlschreiber
## 610     0.19418297    0.148545401             0.57            David Ferrer
## 611     0.15090131    0.106635878             0.56            Ivo Karlovic
## 612     0.08539805    0.015821248             0.56            David Ferrer
## 613     0.09529775    0.067213191             0.56           Andreas Seppi
## 614     0.15469560    0.102882333             0.56         Richard Gasquet
## 615     0.13289098    0.067531889             0.56           Stan Wawrinka
## 616     0.24019251    0.208392705             0.56        Marcos Baghdatis
## 617     0.13134908    0.073331182             0.56      Jo-Wilfried Tsonga
## 618     0.07807274    0.022786962             0.56   Philipp Kohlschreiber
## 619     0.24414498    0.204268540             0.56       Fernando Verdasco
## 620     0.20255066    0.148241917             0.55   Philipp Kohlschreiber
## 621     0.08115293    0.025351490             0.55              Ivan Dodig
## 622     0.30842283    0.257445320             0.54           Roger Federer
## 623     0.07704486    0.042075868             0.54            Ivo Karlovic
## 624     0.14774069    0.065759215             0.54             Juan Monaco
## 625     0.19981711    0.168653028             0.54             Marin Cilic
## 626     0.21292658    0.157793558             0.54         Grigor Dimitrov
## 627     0.20353119    0.133194953             0.54           Tomas Berdych
## 628     0.07408701    0.031965947             0.53     Alexandr Dolgopolov
## 629     0.12435944    0.043523143             0.53          Lleyton Hewitt
## 630     0.30151169    0.199432341             0.53            David Ferrer
## 631     0.09349383    0.064905754             0.53            Ivo Karlovic
## 632     0.12800206    0.024786188             0.53          Kevin Anderson
## 633     0.33927060    0.269243383             0.53            Rafael Nadal
## 634     0.42915851    0.363772172             0.53            Rafael Nadal
## 635     0.22310880    0.175143747             0.53            Rafael Nadal
## 636     0.23643437    0.171358875             0.52           Roger Federer
## 637     0.10211098    0.044105139             0.52      Jo-Wilfried Tsonga
## 638     0.17152073    0.117569113             0.52        Marcos Baghdatis
## 639     0.14079089    0.080351640             0.51        Santiago Giraldo
## 640     0.16939040    0.115180246             0.51      Jo-Wilfried Tsonga
## 641     0.07908737    0.043356000             0.51         Richard Gasquet
## 642     0.13741279    0.091916274             0.50              Tommy Haas
## 643     0.09985490    0.033863604             0.50         Nicolas Almagro
## 644     0.24945386    0.199475706             0.50            David Ferrer
## 645     0.13988589    0.079091978             0.50            Gilles Simon
## 646     0.08615514    0.049949971             0.50          Vasek Pospisil
## 647     0.07098038    0.021001299             0.50             Marin Cilic
## 648     0.19950119    0.143524466             0.50           Roger Federer
## 649     0.14228372    0.096592371             0.50          Carlos Berlocq
## 650     0.12910453    0.083940348             0.50     Alexandr Dolgopolov
## 651     0.12216951    0.069801601             0.50         Nicolas Almagro
## 652     0.21466861    0.157984074             0.50        Santiago Giraldo
## 653     0.26975325    0.210498096             0.50            Rafael Nadal
## 654     0.09257630    0.070724774             0.50          Kevin Anderson
## 655     0.12959073    0.084103857             0.49             Andy Murray
## 656     0.07144538    0.042681749             0.49           Stan Wawrinka
## 657     0.09907423    0.025310854             0.49           Denis Istomin
## 658     0.07332494    0.015307377             0.48          Ernests Gulbis
## 659     0.10095092    0.071195486             0.48             Juan Monaco
## 660     0.20897649    0.159963930             0.48             Andy Murray
## 661     0.17796033    0.106327603             0.48   Philipp Kohlschreiber
## 662     0.16519886    0.101786678             0.47             Juan Monaco
## 663     0.11692189    0.048538916             0.47              Tommy Haas
## 664     0.27369653    0.195715108             0.47           Roger Federer
## 665     0.10365550    0.058608340             0.47            David Ferrer
## 666     0.22945644    0.179274548             0.47       Fernando Verdasco
## 667     0.18463488    0.119723377             0.46          Viktor Troicki
## 668     0.06509078    0.021018060             0.45             Sam Querrey
## 669     0.14641475    0.091070588             0.45           Tomas Berdych
## 670     0.08854643    0.028488696             0.45           Tomas Berdych
## 671     0.07592657    0.046245836             0.45           Andreas Seppi
## 672     0.09037908    0.044946616             0.44          Radek Stepanek
## 673     0.08459433    0.031870990             0.44   Roberto Bautista Agut
## 674     0.19630404    0.138150374             0.44           Tommy Robredo
## 675     0.07785094    0.040425556             0.44            David Ferrer
## 676     0.14057729    0.093053235             0.44            Gilles Simon
## 677     0.07125886    0.041501668             0.44             Juan Monaco
## 678     0.07073154    0.011246453             0.44             Andy Murray
## 679     0.09158387    0.030940322             0.44             Marin Cilic
## 680     0.08107356    0.028153879             0.43            Gael Monfils
## 681     0.19313726    0.125918263             0.42            David Ferrer
## 682     0.14406348    0.087665985             0.42       Fernando Verdasco
## 683     0.13943567    0.091290505             0.42            Gael Monfils
## 684     0.22201095    0.170376682             0.42       Fernando Verdasco
## 685     0.07797845    0.017247271             0.42          Viktor Troicki
## 686     0.10818795    0.053558965             0.42            Rafael Nadal
## 687     0.08765739    0.034040472             0.42      Jo-Wilfried Tsonga
## 688     0.18633605    0.136209171             0.42          Viktor Troicki
## 689     0.13073978    0.090642624             0.41         Richard Gasquet
## 690     0.10407828    0.064926564             0.41           Pablo Andujar
## 691     0.08390741    0.030096401             0.41         Richard Gasquet
## 692     0.11921398    0.079525543             0.41           Tommy Robredo
## 693     0.18148597    0.139589309             0.41             Marin Cilic
## 694     0.18993581    0.130439022             0.40            David Ferrer
## 695     0.23895951    0.185861244             0.40            David Ferrer
## 696     0.16615694    0.124508475             0.40            David Ferrer
## 697     0.24959093    0.196037032             0.40          Kevin Anderson
## 698     0.11201721    0.072302314             0.40             Juan Monaco
## 699     0.10511623    0.034073040             0.40            David Ferrer
## 700     0.12145469    0.089413130             0.40           Roger Federer
## 701     0.06580341    0.027739000             0.40            David Ferrer
## 702     0.13163183    0.075050236             0.40            Gael Monfils
## 703     0.09439518    0.031858314             0.40            David Ferrer
## 704     0.14332058    0.086154548             0.40       Fernando Verdasco
## 705     0.18782901    0.136922049             0.40          Ernests Gulbis
## 706     0.13269994    0.084155653             0.40          Ernests Gulbis
## 707     0.07840781    0.047596159             0.40   Roberto Bautista Agut
## 708     0.09411927    0.070673853             0.40           Tomas Berdych
## 709     0.09204578    0.044907113             0.39           Roger Federer
## 710     0.10429562    0.048280629             0.38   Philipp Kohlschreiber
## 711     0.11980886    0.079236076             0.38         Richard Gasquet
## 712     0.09092594    0.051399634             0.38           Roger Federer
## 713     0.15191324    0.110177257             0.38            Ivo Karlovic
## 714     0.22549538    0.181093374             0.38       Federico Delbonis
## 715     0.27050722    0.233412123             0.37       Fernando Verdasco
## 716     0.16581883    0.123270702             0.37             Andy Murray
## 717     0.17703500    0.134077516             0.37             Andy Murray
## 718     0.14287437    0.092821480             0.37           Tomas Berdych
## 719     0.14133457    0.099680022             0.37            Gael Monfils
## 720     0.12387201    0.090816950             0.36   Philipp Kohlschreiber
## 721     0.08972469    0.049661278             0.36             Marin Cilic
## 722     0.09434871    0.070208667             0.36         Richard Gasquet
## 723     0.10682925    0.074275451             0.36            David Ferrer
## 724     0.14026866    0.089962688             0.36      Jo-Wilfried Tsonga
## 725     0.06807195    0.012690440             0.35            Gilles Simon
## 726     0.07695002    0.037062984             0.35              Tommy Haas
## 727     0.21908469    0.173933409             0.35       Nikolay Davydenko
## 728     0.14003955    0.097815862             0.35           Roger Federer
## 729     0.08397580    0.043828544             0.35       Fernando Verdasco
## 730     0.19668491    0.152363245             0.35            Rafael Nadal
## 731     0.18300515    0.130034769             0.34           Roger Federer
## 732     0.08729980    0.062957270             0.34            Rafael Nadal
## 733     0.18858594    0.144235718             0.34            Rafael Nadal
## 734     0.21031332    0.174184568             0.34          Carlos Berlocq
## 735     0.09553535    0.071008443             0.34           Roger Federer
## 736     0.07416136    0.009550147             0.33              Tommy Haas
## 737     0.17761380    0.106779891             0.33             Juan Monaco
## 738     0.16969465    0.116926466             0.33       Fernando Verdasco
## 739     0.06090284    0.021019276             0.33           Stan Wawrinka
## 740     0.11903824    0.093796779             0.33             Andy Murray
## 741     0.07443117    0.042117449             0.33             Juan Monaco
## 742     0.09983751    0.050220784             0.33         Richard Gasquet
## 743     0.08568377    0.061194660             0.33   Philipp Kohlschreiber
## 744     0.08426201    0.035347938             0.33            David Ferrer
## 745     0.13338561    0.073281830             0.32            David Ferrer
## 746     0.21115382    0.146925963             0.32          Novak Djokovic
## 747     0.10804211    0.066070818             0.32           Roger Federer
## 748     0.12817916    0.102538723             0.32             Andy Murray
## 749     0.11501484    0.064332350             0.32           Roger Federer
## 750     0.07393036    0.041138590             0.31         Mikhail Youzhny
## 751     0.13908650    0.104305238             0.31             Juan Monaco
## 752     0.15982861    0.106706692             0.31            Rafael Nadal
## 753     0.09352158    0.060131603             0.31          Novak Djokovic
## 754     0.12016458    0.059848030             0.30       Fernando Verdasco
## 755     0.11970141    0.059409799             0.30         Richard Gasquet
## 756     0.11017262    0.067473668             0.30           Roger Federer
## 757     0.23220127    0.146895032             0.30            Rafael Nadal
## 758     0.15552711    0.093306419             0.30          Novak Djokovic
## 759     0.13098870    0.087489132             0.30            David Ferrer
## 760     0.15741062    0.121797984             0.30            Rafael Nadal
## 761     0.22688816    0.188845115             0.29            Rafael Nadal
## 762     0.06164924    0.028729888             0.29           Andreas Seppi
## 763     0.08176826    0.031453460             0.29             Andy Murray
## 764     0.07413036    0.040563789             0.28             Marin Cilic
## 765     0.11815355    0.091946826             0.28            David Ferrer
## 766     0.07276501    0.038977133             0.27         Mikhail Youzhny
## 767     0.06511402    0.039953848             0.27           Roger Federer
## 768     0.07136135    0.046053600             0.27           Roger Federer
## 769     0.13075630    0.085885022             0.26         Richard Gasquet
## 770     0.07450910    0.040397698             0.26             Marin Cilic
## 771     0.07956234    0.019586653             0.26             Marin Cilic
## 772     0.07126045    0.036980119             0.25           Tomas Berdych
## 773     0.08897404    0.062838666             0.25        Santiago Giraldo
## 774     0.06566982    0.031293372             0.24              John Isner
## 775     0.08212660    0.047219290             0.24          Novak Djokovic
## 776     0.09636665    0.060712449             0.23          Novak Djokovic
## 777     0.12676118    0.080957884             0.23           Roger Federer
## 778     0.09009467    0.045418657             0.22          Novak Djokovic
## 779     0.09507557    0.050195424             0.22            David Ferrer
## 780     0.09752878    0.061544229             0.22           Roger Federer
## 781     0.09771001    0.070717137             0.22       Fernando Verdasco
## 782     0.07623877    0.032130619             0.22            Milos Raonic
## 783     0.15087973    0.122579411             0.22            Rafael Nadal
## 784     0.06189564    0.018015653             0.21             Andy Murray
## 785     0.07268338    0.046087929             0.21           Roger Federer
## 786     0.08830582    0.061323030             0.21             Andy Murray
## 787     0.16931535    0.130660302             0.21            Rafael Nadal
## 788     0.16880314    0.129843038             0.20            Rafael Nadal
## 789     0.09465456    0.030799711             0.20            Rafael Nadal
## 790     0.07985984    0.043864508             0.20      Jo-Wilfried Tsonga
## 791     0.06679410    0.040124247             0.20           Roger Federer
## 792     0.06700832    0.031441373             0.20           Tomas Berdych
## 793     0.12516392    0.097034818             0.20            Rafael Nadal
## 794     0.07703767    0.041136412             0.20          Novak Djokovic
## 795     0.15493544    0.116437590             0.20            Rafael Nadal
## 796     0.07316199    0.045878215             0.18           Stan Wawrinka
## 797     0.13537854    0.087269277             0.18            Rafael Nadal
## 798     0.08391655    0.056359350             0.18            Rafael Nadal
## 799     0.10516915    0.076831478             0.17            Rafael Nadal
## 800     0.07084861    0.024289978             0.15             Andy Murray
## 801     0.07479169    0.046753645             0.15          Novak Djokovic
## 802     0.07024437    0.051631429             0.15           Roger Federer
## 803     0.07730134    0.021094314             0.15            Rafael Nadal
## 804     0.10947113    0.070880825             0.15            Rafael Nadal
## 805     0.08401234    0.026959059             0.14           Tomas Berdych
## 806     0.06664251    0.038572970             0.14             Andy Murray
## 807     0.07056557    0.014220010             0.14            Rafael Nadal
## 808     0.10514533    0.066025139             0.13             Andy Murray
## 809     0.08538932    0.066007370             0.12            Rafael Nadal
## 810     0.06524706    0.026859779             0.11           Roger Federer
## 811     0.07006136    0.041140780             0.11            Rafael Nadal
## 812     0.07212009    0.062461355             0.11            Rafael Nadal
## 813     0.06876956    0.049159109             0.09             Andy Murray
##     posterior_mean_clay_skill_winner posterior_mean_grass_skill_winner
## 1                       -0.106824587                      0.0855466798
## 2                       -0.078035808                     -0.0614711611
## 3                        0.122401846                      0.2304844855
## 4                        0.045104598                      0.2092389197
## 5                        0.135810667                      0.0240543883
## 6                       -0.232801741                      0.0607091630
## 7                        0.297624337                      0.2307802512
## 8                        0.094927071                      0.0393148631
## 9                        0.100053858                      0.1436033605
## 10                       0.154936835                      0.2061834276
## 11                       0.568721559                      0.2842440160
## 12                       0.588720065                      0.3409339903
## 13                      -0.022671627                     -0.0793749274
## 14                       0.544488241                      0.2663760407
## 15                      -0.026804256                     -0.0568267521
## 16                       0.225796740                      0.1835085976
## 17                       0.367790270                      0.2031778337
## 18                       0.141334857                     -0.0281450111
## 19                       0.324438107                      0.3554108001
## 20                      -0.056257272                      0.0719347001
## 21                       0.028487069                     -0.1049496864
## 22                      -0.025204673                     -0.0986497651
## 23                      -0.029313916                      0.0536465234
## 24                      -0.228974678                     -0.0644490825
## 25                      -0.199351140                     -0.0349461707
## 26                       0.115360398                     -0.0443825300
## 27                      -0.184265421                     -0.0534347724
## 28                       0.297624337                      0.2307802512
## 29                       0.051336067                     -0.0328792661
## 30                       0.143151429                      0.1158426959
## 31                      -0.240451851                     -0.0569577032
## 32                       0.178967057                      0.3597204743
## 33                      -0.081736549                      0.0334062145
## 34                       0.038233854                      0.1022505396
## 35                       0.147846501                      0.1484938054
## 36                       0.192251492                      0.1919988494
## 37                       0.003618868                     -0.0676743323
## 38                      -0.044588738                      0.0127912436
## 39                       0.020662490                     -0.1168965633
## 40                      -0.034351654                     -0.1114511027
## 41                       0.127204570                      0.1426610261
## 42                       0.033095410                      0.0438012633
## 43                       0.097797848                      0.0319186659
## 44                       0.146552455                     -0.0228667668
## 45                       0.586069450                      0.3517684361
## 46                       0.246233922                      0.2281862233
## 47                       0.147462409                      0.1374164593
## 48                       0.120616071                      0.0294404522
## 49                       0.025130610                     -0.0763013550
## 50                       0.177252748                      0.1651551455
## 51                       0.129045716                      0.0447469060
## 52                      -0.043530387                     -0.0177898805
## 53                       0.123064530                      0.1463432186
## 54                      -0.160956967                      0.1161994902
## 55                       0.078511148                      0.0481373489
## 56                       0.567814908                      0.5454277110
## 57                       0.226119502                      0.1832424065
## 58                       0.042719858                      0.2074397565
## 59                      -0.292022580                     -0.0386367069
## 60                      -0.030002207                     -0.1109166433
## 61                      -0.025329917                     -0.1061347480
## 62                      -0.014797186                     -0.0733614046
## 63                       0.130405133                      0.1412760243
## 64                      -0.028517829                      0.0676077693
## 65                       0.019579663                      0.1325082047
## 66                       0.455257443                      0.5760322504
## 67                       0.191923448                      0.2601681254
## 68                       0.101357535                      0.0592016931
## 69                       0.004298392                      0.0786725814
## 70                       0.202535857                      0.1830776791
## 71                       0.021540297                      0.1394083071
## 72                       0.152596571                      0.1566002659
## 73                      -0.043534322                      0.0387741842
## 74                       0.320437707                      0.1411030656
## 75                      -0.013507465                     -0.0752138454
## 76                       0.014102513                      0.0592791089
## 77                       0.162815312                      0.1288950052
## 78                       0.003207427                     -0.0590768773
## 79                       0.187703924                      0.2278274868
## 80                      -0.101542184                      0.0415156056
## 81                       0.040813780                      0.0045213688
## 82                      -0.281928491                      0.0273167906
## 83                       0.009371784                      0.0613675746
## 84                      -0.221796346                     -0.1581650567
## 85                       0.133152690                      0.0316874413
## 86                       0.140915722                      0.2121465649
## 87                       0.209829327                      0.1135702791
## 88                       0.015481790                      0.0889013097
## 89                       0.036958632                      0.1296065461
## 90                       0.007725351                      0.1023169114
## 91                       0.025837032                     -0.1111131331
## 92                       0.052255049                     -0.0226134040
## 93                       0.557437657                      0.5681408470
## 94                      -0.029159730                     -0.1156461140
## 95                       0.458848704                      0.5779215046
## 96                       0.327404106                      0.2394418019
## 97                      -0.228974678                     -0.0644490825
## 98                       0.146552455                     -0.0228667668
## 99                       0.026388202                      0.2073343486
## 100                     -0.062396750                     -0.0695384470
## 101                      0.354574672                      0.3591064108
## 102                      0.034341633                      0.1251247007
## 103                      0.071036464                      0.2171785229
## 104                      0.227253099                      0.1843127049
## 105                      0.156651939                      0.0870486881
## 106                     -0.024101317                     -0.0320803625
## 107                      0.578884073                      0.5506342994
## 108                     -0.026384294                      0.0247490492
## 109                      0.049603337                     -0.2919003582
## 110                     -0.170058684                     -0.1979689037
## 111                      0.214749343                      0.1819876192
## 112                      0.009119366                     -0.0786292380
## 113                      0.015895243                      0.0636107071
## 114                      0.078511148                      0.0481373489
## 115                      0.084198556                     -0.0234626492
## 116                      0.118663484                     -0.0486344095
## 117                     -0.049811448                      0.0089147439
## 118                      0.034341633                      0.1251247007
## 119                      0.590536332                      0.5532159453
## 120                     -0.160956967                      0.1161994902
## 121                      0.019579663                      0.1325082047
## 122                     -0.099140452                      0.0844682995
## 123                      0.120081645                      0.1832607499
## 124                      0.191923448                      0.2601681254
## 125                      0.078198065                      0.0622334039
## 126                      0.004356127                     -0.0597467147
## 127                      0.178985948                      0.1915099572
## 128                      0.189194094                      0.1467084701
## 129                      0.161015507                      0.0217265869
## 130                      0.104505858                      0.0206820636
## 131                      0.136704946                      0.1323519558
## 132                     -0.061675608                      0.0604037949
## 133                     -0.017690311                     -0.0849172965
## 134                      0.376230276                      0.3647206699
## 135                      0.120616071                      0.0294404522
## 136                      0.181868122                      0.1438658615
## 137                      0.029559068                      0.1168949541
## 138                      0.390581314                      0.1905334644
## 139                      0.134117386                      0.1190321158
## 140                      0.043620221                      0.0922250662
## 141                      0.319194997                      0.1211457154
## 142                     -0.021354100                     -0.0376359079
## 143                      0.096297693                      0.0612928306
## 144                      0.131326027                      0.1425300453
## 145                     -0.052772976                      0.1768048703
## 146                      0.146327091                      0.1157073226
## 147                      0.129549413                      0.2101364709
## 148                     -0.054983130                     -0.0163834625
## 149                      0.072340874                     -0.0431673656
## 150                      0.135754087                      0.1272606124
## 151                     -0.161628356                     -0.0571402322
## 152                      0.226438731                      0.0398917279
## 153                      0.021540297                      0.1394083071
## 154                      0.121078179                     -0.0334851796
## 155                      0.033245314                     -0.0113159614
## 156                      0.078511148                      0.0481373489
## 157                      0.208910045                      0.1848141474
## 158                      0.115160458                     -0.0270884143
## 159                      0.147172158                      0.0432595189
## 160                     -0.011233315                     -0.1057497536
## 161                     -0.062878407                     -0.0071959748
## 162                     -0.059760290                     -0.0284750857
## 163                     -0.069513973                      0.1318309893
## 164                     -0.152218584                     -0.2928719824
## 165                      0.126268347                      0.0804626725
## 166                      0.039939091                     -0.2552244922
## 167                      0.354574672                      0.3591064108
## 168                     -0.058687811                     -0.0829600543
## 169                      0.589189540                      0.5594838288
## 170                     -0.098160121                     -0.1288280078
## 171                     -0.095664256                      0.1044309228
## 172                      0.097201231                      0.2117150582
## 173                     -0.106184497                      0.0861823601
## 174                      0.019667487                      0.1222191682
## 175                     -0.078085480                     -0.0858370699
## 176                      0.133247797                      0.2194400514
## 177                      0.190913804                      0.1570750293
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## 618                      0.227795413                      0.2233711090
## 619                      0.331534605                      0.2365112455
## 620                      0.234387053                      0.1867701469
## 621                     -0.072838559                      0.0491984063
## 622                      0.583011670                      0.5693515628
## 623                      0.042719858                      0.2074397565
## 624                      0.312419859                      0.1345965300
## 625                      0.307183929                      0.3141726165
## 626                      0.186948744                      0.1282881590
## 627                      0.414303460                      0.3747657802
## 628                      0.134117386                      0.1190321158
## 629                      0.186840953                      0.2900432327
## 630                      0.586069450                      0.3517684361
## 631                      0.044071160                      0.2119227836
## 632                      0.144463240                      0.1441288407
## 633                      0.879578437                      0.4522869949
## 634                      0.879578437                      0.4522869949
## 635                      0.879578437                      0.4522869949
## 636                      0.596813489                      0.5610149442
## 637                      0.354574672                      0.3591064108
## 638                      0.071036464                      0.2171785229
## 639                      0.104977847                      0.0220285621
## 640                      0.375340458                      0.3600087647
## 641                      0.333674769                      0.2982594454
## 642                      0.159807392                      0.1944037619
## 643                      0.336708226                      0.0630716790
## 644                      0.580686158                      0.2834552548
## 645                      0.221006488                      0.1902102883
## 646                     -0.039526315                      0.0098560519
## 647                      0.314562755                      0.2781967055
## 648                      0.587289226                      0.5591396953
## 649                      0.128421970                     -0.0722682542
## 650                      0.159127442                      0.1404112144
## 651                      0.358721013                      0.1389267411
## 652                      0.089276772                      0.0176802117
## 653                      0.879578437                      0.4522869949
## 654                      0.190913804                      0.1570750293
## 655                      0.484347610                      0.5373891314
## 656                      0.335762610                      0.2338210973
## 657                     -0.054307103                      0.1411566891
## 658                      0.186121831                      0.0261221857
## 659                      0.326925714                      0.1344234002
## 660                      0.488002242                      0.5560149757
## 661                      0.225044136                      0.2229799690
## 662                      0.315170657                      0.0896758979
## 663                      0.219060747                      0.1887779584
## 664                      0.583011670                      0.5693515628
## 665                      0.586069450                      0.3517684361
## 666                      0.372453593                      0.2013861235
## 667                      0.161242222                      0.1147929750
## 668                      0.112460143                      0.2410388961
## 669                      0.426237783                      0.3468755756
## 670                      0.407566966                      0.3620393122
## 671                      0.148191057                      0.1026762858
## 672                      0.171805060                      0.1998759820
## 673                     -0.232586361                     -0.2164180745
## 674                      0.244219832                      0.0478932522
## 675                      0.586983334                      0.3516320118
## 676                      0.225796740                      0.1835085976
## 677                      0.320153177                      0.1356496608
## 678                      0.458848704                      0.5779215046
## 679                      0.306287064                      0.3128205622
## 680                      0.246539842                      0.2284103832
## 681                      0.568721559                      0.2842440160
## 682                      0.385267967                      0.2041284178
## 683                      0.251307312                      0.2321104563
## 684                      0.371378664                      0.2062928177
## 685                      0.159971938                      0.1170807694
## 686                      0.892953752                      0.4534912367
## 687                      0.354574672                      0.3591064108
## 688                      0.143455293                      0.1119726979
## 689                      0.322266442                      0.2482783672
## 690                      0.039939091                     -0.2552244922
## 691                      0.337001493                      0.2872150574
## 692                      0.250609472                      0.0679963067
## 693                      0.306287064                      0.3128205622
## 694                      0.551436798                      0.2796776589
## 695                      0.568995872                      0.2760711859
## 696                      0.580686158                      0.2834552548
## 697                      0.145458529                      0.1435562295
## 698                      0.326925714                      0.1344234002
## 699                      0.585697198                      0.3505532840
## 700                      0.587289226                      0.5591396953
## 701                      0.585697198                      0.3505532840
## 702                      0.246539842                      0.2284103832
## 703                      0.587097183                      0.3591331033
## 704                      0.369135333                      0.2019972657
## 705                      0.172821868                      0.1051015172
## 706                      0.205214185                      0.1001117726
## 707                      0.024138137                      0.0207670063
## 708                      0.414303460                      0.3747657802
## 709                      0.582782078                      0.5569013778
## 710                      0.231916998                      0.1881619520
## 711                      0.318645924                      0.2445673211
## 712                      0.596813489                      0.5610149442
## 713                      0.026388202                      0.2073343486
## 714                      0.160540522                      0.0385226405
## 715                      0.383163555                      0.2073122613
## 716                      0.484347610                      0.5373891314
## 717                      0.488657041                      0.5539723734
## 718                      0.428644481                      0.3566571733
## 719                      0.256076316                      0.2487695653
## 720                      0.234387053                      0.1867701469
## 721                      0.316907467                      0.2805107152
## 722                      0.325937534                      0.2830453989
## 723                      0.568624739                      0.3614752519
## 724                      0.378667408                      0.3650657704
## 725                      0.175933385                      0.1917963130
## 726                      0.159807392                      0.1944037619
## 727                      0.334323305                      0.2225028225
## 728                      0.583011670                      0.5693515628
## 729                      0.371378664                      0.2062928177
## 730                      0.880750520                      0.4513261050
## 731                      0.568877035                      0.5489946272
## 732                      0.884642489                      0.4541345651
## 733                      0.917632146                      0.4538779807
## 734                      0.156809267                     -0.0345551804
## 735                      0.553561910                      0.5678128737
## 736                      0.159807392                      0.1944037619
## 737                      0.327362535                      0.1120843043
## 738                      0.385267967                      0.2041284178
## 739                      0.338120807                      0.2237346144
## 740                      0.487150520                      0.5566484105
## 741                      0.321044412                      0.1410270431
## 742                      0.328215800                      0.2703910144
## 743                      0.227789989                      0.2256981143
## 744                      0.582062150                      0.3485975801
## 745                      0.580686158                      0.2834552548
## 746                      0.660660142                      0.5436723968
## 747                      0.590275105                      0.5563758395
## 748                      0.487897012                      0.5560244907
## 749                      0.585135586                      0.5578851081
## 750                      0.186986515                      0.2355842014
## 751                      0.326925714                      0.1344234002
## 752                      0.874127806                      0.4402121938
## 753                      0.666305703                      0.5831720835
## 754                      0.390581314                      0.1905334644
## 755                      0.319594537                      0.2492300047
## 756                      0.587289226                      0.5591396953
## 757                      0.919499934                      0.4517577341
## 758                      0.668083695                      0.5641826436
## 759                      0.587097183                      0.3591331033
## 760                      0.879578437                      0.4522869949
## 761                      0.915757530                      0.4485120471
## 762                      0.159121781                      0.0548719167
## 763                      0.488657041                      0.5539723734
## 764                      0.306287064                      0.3128205622
## 765                      0.583963612                      0.3450735048
## 766                      0.188135835                      0.2319379447
## 767                      0.590536332                      0.5532159453
## 768                      0.590536332                      0.5532159453
## 769                      0.328215800                      0.2703910144
## 770                      0.305592053                      0.2830664791
## 771                      0.307183929                      0.3141726165
## 772                      0.426237783                      0.3468755756
## 773                      0.104977847                      0.0220285621
## 774                      0.179366480                      0.1958898898
## 775                      0.665523893                      0.5608121513
## 776                      0.664516098                      0.5605979736
## 777                      0.590536332                      0.5532159453
## 778                      0.660115655                      0.5222644360
## 779                      0.583772353                      0.3325986985
## 780                      0.587289226                      0.5591396953
## 781                      0.372453593                      0.2013861235
## 782                      0.258502147                      0.2663409564
## 783                      0.880750520                      0.4513261050
## 784                      0.481619909                      0.5392935810
## 785                      0.590536332                      0.5532159453
## 786                      0.488657041                      0.5539723734
## 787                      0.873413127                      0.4394133318
## 788                      0.862888063                      0.4376865148
## 789                      0.915757530                      0.4485120471
## 790                      0.321237135                      0.3582958814
## 791                      0.590536332                      0.5532159453
## 792                      0.426734070                      0.3516898938
## 793                      0.884642489                      0.4541345651
## 794                      0.661103862                      0.5704514580
## 795                      0.873413127                      0.4394133318
## 796                      0.358245649                      0.2400878448
## 797                      0.880750520                      0.4513261050
## 798                      0.873413127                      0.4394133318
## 799                      0.879578437                      0.4522869949
## 800                      0.484919530                      0.5371510630
## 801                      0.663484221                      0.5258298615
## 802                      0.587289226                      0.5591396953
## 803                      0.893934509                      0.4586090346
## 804                      0.892953752                      0.4534912367
## 805                      0.422143423                      0.3495384833
## 806                      0.488657041                      0.5539723734
## 807                      0.917722130                      0.4542628695
## 808                      0.478525414                      0.5363318439
## 809                      0.917632146                      0.4538779807
## 810                      0.567814908                      0.5454277110
## 811                      0.917722130                      0.4542628695
## 812                      0.873413127                      0.4394133318
## 813                      0.488002242                      0.5560149757
##     posterior_mean_hard_skill_winner posterior_sd_clay_skill_winner
## 1                       0.0677096406                     0.06745985
## 2                      -0.0823947980                     0.09031717
## 3                       0.2003409145                     0.05260695
## 4                       0.1695905597                     0.07004510
## 5                       0.0140695124                     0.05911125
## 6                      -0.0093270058                     0.08127090
## 7                       0.2843382520                     0.05397695
## 8                       0.0499525843                     0.05361226
## 9                       0.1384266793                     0.04110992
## 10                      0.2210957841                     0.06069596
## 11                      0.4044632005                     0.04436428
## 12                      0.4126711280                     0.03197033
## 13                     -0.0814601594                     0.09991875
## 14                      0.3828821270                     0.04809144
## 15                     -0.0820489865                     0.06217833
## 16                      0.2465311135                     0.04743448
## 17                      0.3212302055                     0.04273853
## 18                     -0.0049297647                     0.05591192
## 19                      0.3647286130                     0.05263435
## 20                      0.0462522894                     0.08804929
## 21                     -0.0865873098                     0.10723535
## 22                     -0.0759671301                     0.13938501
## 23                      0.0522745442                     0.13734189
## 24                     -0.1206100182                     0.10539939
## 25                     -0.1171910651                     0.13845845
## 26                     -0.0574049053                     0.06613040
## 27                     -0.1321896281                     0.14781315
## 28                      0.2843382520                     0.05397695
## 29                     -0.0367433297                     0.07050264
## 30                      0.1580132649                     0.04194229
## 31                     -0.0828801544                     0.10398002
## 32                      0.3398640335                     0.06055148
## 33                      0.0234792622                     0.07789774
## 34                      0.0737285257                     0.04402520
## 35                      0.1212294677                     0.05462285
## 36                      0.1677260348                     0.07889400
## 37                     -0.0898095256                     0.06024487
## 38                      0.0189514398                     0.06834304
## 39                     -0.0983886422                     0.08160368
## 40                     -0.1330761589                     0.07116971
## 41                      0.1806747137                     0.08210436
## 42                      0.0366648573                     0.07230866
## 43                      0.0463450991                     0.05462129
## 44                      0.0101812584                     0.06207079
## 45                      0.4190564520                     0.04160549
## 46                      0.2810575265                     0.05482163
## 47                      0.1609771348                     0.05245654
## 48                      0.0521557339                     0.05649631
## 49                     -0.0658457147                     0.10931561
## 50                      0.1732933003                     0.04918036
## 51                      0.0437132690                     0.06962695
## 52                     -0.0249122184                     0.09004648
## 53                      0.1222974368                     0.09486701
## 54                     -0.0044519312                     0.08942805
## 55                      0.0502538342                     0.05481053
## 56                      0.6323826765                     0.05526135
## 57                      0.2541898375                     0.04783845
## 58                      0.1672592521                     0.06777900
## 59                     -0.0607312223                     0.11339908
## 60                     -0.1081750625                     0.07635973
## 61                     -0.0774153684                     0.13265245
## 62                     -0.0551381550                     0.14099565
## 63                      0.1584620764                     0.05141098
## 64                      0.0481587798                     0.12955964
## 65                      0.1445580734                     0.06738366
## 66                      0.5660741855                     0.05014104
## 67                      0.2635164815                     0.04375532
## 68                      0.0514305144                     0.05461286
## 69                      0.0739844944                     0.14369869
## 70                      0.2538302505                     0.05877330
## 71                      0.0950135674                     0.04696526
## 72                      0.1346354975                     0.05451085
## 73                      0.0341766241                     0.13348884
## 74                      0.2025330251                     0.04158094
## 75                     -0.0768166481                     0.10116964
## 76                      0.0438708651                     0.06183033
## 77                      0.1824893410                     0.05021256
## 78                     -0.0800787899                     0.06094507
## 79                      0.2748463515                     0.05073902
## 80                      0.0435523437                     0.08728441
## 81                      0.0269154278                     0.08795435
## 82                     -0.0183876025                     0.09374478
## 83                      0.0737581799                     0.10377095
## 84                     -0.1979620509                     0.09889474
## 85                      0.0523173865                     0.08310220
## 86                      0.2097811649                     0.08072393
## 87                      0.1620305689                     0.05330149
## 88                      0.0483930594                     0.05175699
## 89                      0.1478390601                     0.05806294
## 90                      0.0599690943                     0.05633049
## 91                     -0.0867422301                     0.11440876
## 92                     -0.0449440908                     0.07380281
## 93                      0.6171637010                     0.04354800
## 94                     -0.1355368216                     0.06671775
## 95                      0.5869394145                     0.05243596
## 96                      0.3141742070                     0.04049138
## 97                     -0.1206100182                     0.10539939
## 98                      0.0101812584                     0.06207079
## 99                      0.1602995565                     0.06724727
## 100                    -0.0588132828                     0.12824583
## 101                     0.3786174960                     0.04925988
## 102                     0.1412841069                     0.05863912
## 103                     0.2387978245                     0.06057718
## 104                     0.2519335415                     0.04722426
## 105                     0.0974983316                     0.09619189
## 106                    -0.0205601827                     0.11856369
## 107                     0.6343192985                     0.05407681
## 108                     0.0388618946                     0.06553893
## 109                    -0.2106264061                     0.05771370
## 110                    -0.2218984146                     0.08516444
## 111                     0.2432081110                     0.04375829
## 112                    -0.0762071105                     0.08706575
## 113                     0.0796166237                     0.10367326
## 114                     0.0502538342                     0.05481053
## 115                     0.0053791757                     0.04857063
## 116                    -0.0113400725                     0.05903063
## 117                    -0.0023747333                     0.08606636
## 118                     0.1412841069                     0.05863912
## 119                     0.6342635020                     0.04904890
## 120                    -0.0044519312                     0.08942805
## 121                     0.1445580734                     0.06738366
## 122                     0.0580006201                     0.05904184
## 123                     0.1260742939                     0.05227786
## 124                     0.2635164815                     0.04375532
## 125                     0.0806717717                     0.15125649
## 126                    -0.0847835926                     0.06282690
## 127                     0.2182592880                     0.05080290
## 128                     0.1307755639                     0.05177182
## 129                     0.0377117589                     0.03958050
## 130                     0.0378849080                     0.04841793
## 131                     0.1432167923                     0.04329390
## 132                     0.0581574521                     0.09466805
## 133                    -0.0819458299                     0.09754458
## 134                     0.3785913540                     0.04744059
## 135                     0.0521557339                     0.05649631
## 136                     0.1932944423                     0.05330053
## 137                     0.0830455734                     0.04681872
## 138                     0.3327106830                     0.04779141
## 139                     0.1368711397                     0.06168182
## 140                     0.1174379008                     0.06434004
## 141                     0.1816250696                     0.03742570
## 142                    -0.0286273982                     0.12485749
## 143                     0.0521500636                     0.05268178
## 144                     0.1552461095                     0.05011582
## 145                     0.1097048380                     0.06935818
## 146                     0.1571238246                     0.04484726
## 147                     0.2546597655                     0.07324489
## 148                    -0.0079010148                     0.12289360
## 149                    -0.0042002793                     0.08354213
## 150                     0.1706615874                     0.06510899
## 151                    -0.0898274661                     0.10927946
## 152                     0.1212562544                     0.05076178
## 153                     0.0950135674                     0.04696526
## 154                    -0.0051298406                     0.06166398
## 155                    -0.0210908012                     0.09399527
## 156                     0.0502538342                     0.05481053
## 157                     0.1975688808                     0.05181352
## 158                     0.0072967410                     0.06422046
## 159                     0.0451708576                     0.06416888
## 160                    -0.1303895341                     0.06619922
## 161                    -0.0197861137                     0.08890359
## 162                    -0.0104501410                     0.07950263
## 163                     0.0217203597                     0.09979954
## 164                    -0.3024570402                     0.06438678
## 165                     0.0889182034                     0.04896247
## 166                    -0.1919157766                     0.04670040
## 167                     0.3786174960                     0.04925988
## 168                    -0.0694304482                     0.12265859
## 169                     0.6365254660                     0.04994356
## 170                    -0.1235265870                     0.08913276
## 171                     0.0067870467                     0.10139484
## 172                     0.2469537035                     0.06700687
## 173                     0.0573144378                     0.06555290
## 174                     0.0897661385                     0.04748686
## 175                    -0.0780488371                     0.12421073
## 176                     0.2356608435                     0.05759615
## 177                     0.1943413841                     0.05421087
## 178                    -0.0694304482                     0.12265859
## 179                     0.2538302505                     0.05877330
## 180                    -0.0487558140                     0.04438188
## 181                     0.1472809236                     0.04607663
## 182                     0.1940977832                     0.03992182
## 183                    -0.0977521741                     0.09677711
## 184                    -0.0427552915                     0.04260014
## 185                    -0.1346415793                     0.09895838
## 186                     0.1672120317                     0.05494986
## 187                     0.0269154278                     0.08795435
## 188                    -0.0312593453                     0.05342015
## 189                    -0.0952934255                     0.09489915
## 190                     0.0817983734                     0.05598135
## 191                    -0.0654086551                     0.03811391
## 192                     0.1428187525                     0.04495303
## 193                     0.1004710887                     0.05520337
## 194                     0.1580161100                     0.06554770
## 195                     0.1456184038                     0.05383222
## 196                     0.1412841069                     0.05863912
## 197                    -0.1189954314                     0.07158206
## 198                     0.2426071600                     0.06377060
## 199                    -0.2472545430                     0.07045925
## 200                    -0.0455234894                     0.04482869
## 201                     0.0381267898                     0.06723692
## 202                     0.0796166237                     0.10367326
## 203                     0.3351912845                     0.04733143
## 204                     0.1499707216                     0.05828548
## 205                    -0.1925193191                     0.09504721
## 206                     0.2160532561                     0.06541618
## 207                     0.4214310845                     0.04033955
## 208                     0.3336078420                     0.05760179
## 209                     0.3229642980                     0.04580746
## 210                     0.1346354975                     0.05451085
## 211                     0.4313536475                     0.04197597
## 212                     0.0756500480                     0.09850436
## 213                     0.1782315678                     0.08337623
## 214                     0.1585156871                     0.09225333
## 215                    -0.0381349598                     0.08049489
## 216                     0.0117447168                     0.08274683
## 217                     0.0760827862                     0.06222425
## 218                     0.0736610164                     0.04726286
## 219                     0.0737581799                     0.10377095
## 220                     0.0968573042                     0.04559250
## 221                     0.3082746170                     0.04706194
## 222                     0.0499525843                     0.05361226
## 223                    -0.0044519312                     0.08942805
## 224                     0.0422179938                     0.08148659
## 225                     0.0615600052                     0.04669634
## 226                     0.1715242072                     0.11512640
## 227                     0.0151987709                     0.13372637
## 228                     0.0479704717                     0.05363717
## 229                    -0.0421618175                     0.07544841
## 230                     0.2241622481                     0.05229728
## 231                     0.1521226161                     0.05922732
## 232                     0.2747998825                     0.04986644
## 233                     0.2834898745                     0.07031578
## 234                     0.0890367875                     0.14047640
## 235                     0.0476219409                     0.08610308
## 236                    -0.0725428345                     0.07262768
## 237                     0.1944195534                     0.03965439
## 238                     0.3330984625                     0.04662563
## 239                    -0.0362505935                     0.07154032
## 240                     0.1843490251                     0.07203481
## 241                     0.5806871495                     0.03970127
## 242                    -0.0847835926                     0.06282690
## 243                     0.1483335845                     0.05893578
## 244                     0.0406764030                     0.04171789
## 245                    -0.0542252083                     0.09146253
## 246                     0.0434591374                     0.05476424
## 247                     0.0152842347                     0.08596218
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## 700                     0.6412496345                     0.05216434
## 701                     0.4144461965                     0.04123565
## 702                     0.2844350510                     0.05641589
## 703                     0.4313536475                     0.04197597
## 704                     0.3130881675                     0.04313585
## 705                     0.1499707216                     0.05828548
## 706                     0.1489544610                     0.05532305
## 707                     0.0021996095                     0.08995154
## 708                     0.4007020560                     0.04304785
## 709                     0.6286976820                     0.04733625
## 710                     0.2132236908                     0.05142978
## 711                     0.2658372030                     0.05222730
## 712                     0.6389784390                     0.04809869
## 713                     0.1602995565                     0.06724727
## 714                     0.0672156207                     0.07618711
## 715                     0.3330984625                     0.04662563
## 716                     0.5765544880                     0.05510547
## 717                     0.5842564470                     0.05610302
## 718                     0.3777031545                     0.04899048
## 719                     0.2886101890                     0.04760750
## 720                     0.2123113703                     0.04958789
## 721                     0.3348721295                     0.04978291
## 722                     0.3066341220                     0.04786831
## 723                     0.4335956755                     0.03875821
## 724                     0.3810259035                     0.04652622
## 725                     0.2505315965                     0.05664426
## 726                     0.1649552124                     0.08810731
## 727                     0.3307848835                     0.05418554
## 728                     0.6375326845                     0.05063673
## 729                     0.3212203245                     0.04205096
## 730                     0.5633731865                     0.04464850
## 731                     0.6359911460                     0.05419646
## 732                     0.5806871495                     0.03970127
## 733                     0.5620962860                     0.04895053
## 734                    -0.0064215971                     0.05060672
## 735                     0.6293388015                     0.04577598
## 736                     0.1649552124                     0.08810731
## 737                     0.1940268143                     0.04148533
## 738                     0.3336780220                     0.04498681
## 739                     0.2806367400                     0.04426879
## 740                     0.5866190855                     0.05471537
## 741                     0.2027911915                     0.03982873
## 742                     0.2863207175                     0.05294082
## 743                     0.2098867420                     0.04405846
## 744                     0.4200090735                     0.03683946
## 745                     0.4039976770                     0.04154090
## 746                     0.6517529080                     0.04896247
## 747                     0.6360524500                     0.04866221
## 748                     0.5819458475                     0.05735877
## 749                     0.6333295280                     0.04824076
## 750                     0.2749854605                     0.05104938
## 751                     0.1930680755                     0.04167817
## 752                     0.5629408935                     0.04131941
## 753                     0.6865522415                     0.04586825
## 754                     0.3327106830                     0.04779141
## 755                     0.2679581365                     0.05211453
## 756                     0.6412496345                     0.05216434
## 757                     0.5610173930                     0.04721836
## 758                     0.6792558785                     0.04927528
## 759                     0.4313536475                     0.04197597
## 760                     0.5791625395                     0.04036911
## 761                     0.5676874890                     0.04825252
## 762                     0.0615600052                     0.04669634
## 763                     0.5842564470                     0.05610302
## 764                     0.3390205805                     0.04476291
## 765                     0.4140684605                     0.03825640
## 766                     0.2738710240                     0.05462119
## 767                     0.6342635020                     0.04904890
## 768                     0.6342635020                     0.04904890
## 769                     0.2863207175                     0.05294082
## 770                     0.3334175075                     0.04604360
## 771                     0.3392070380                     0.04570788
## 772                     0.3724403425                     0.04781574
## 773                     0.0400171673                     0.04915022
## 774                     0.2264985985                     0.05070142
## 775                     0.6732421510                     0.04911496
## 776                     0.6674713025                     0.04854025
## 777                     0.6342635020                     0.04904890
## 778                     0.6534773190                     0.05616659
## 779                     0.4084375465                     0.04061636
## 780                     0.6412496345                     0.05216434
## 781                     0.3238663615                     0.04277745
## 782                     0.3037086435                     0.06822470
## 783                     0.5633731865                     0.04464850
## 784                     0.5779055345                     0.06252109
## 785                     0.6342635020                     0.04904890
## 786                     0.5842564470                     0.05610302
## 787                     0.5614082335                     0.04063577
## 788                     0.5552014550                     0.05288877
## 789                     0.5676874890                     0.04825252
## 790                     0.3696303080                     0.05328868
## 791                     0.6342635020                     0.04904890
## 792                     0.3765068310                     0.04850519
## 793                     0.5806871495                     0.03970127
## 794                     0.6872613340                     0.05014290
## 795                     0.5614082335                     0.04063577
## 796                     0.2993899265                     0.04066401
## 797                     0.5633731865                     0.04464850
## 798                     0.5614082335                     0.04063577
## 799                     0.5791625395                     0.04036911
## 800                     0.5836208685                     0.06318557
## 801                     0.6516472910                     0.04883553
## 802                     0.6412496345                     0.05216434
## 803                     0.5641213490                     0.04615653
## 804                     0.5685287235                     0.04543984
## 805                     0.3728193580                     0.04901588
## 806                     0.5842564470                     0.05610302
## 807                     0.5641230360                     0.04745263
## 808                     0.5821986470                     0.06219879
## 809                     0.5620962860                     0.04895053
## 810                     0.6323826765                     0.05526135
## 811                     0.5641230360                     0.04745263
## 812                     0.5614082335                     0.04063577
## 813                     0.5866873735                     0.05538363
##     posterior_sd_grass_skill_winner posterior_sd_hard_skill_winner
## 1                        0.08006634                     0.04758902
## 2                        0.10077660                     0.08374911
## 3                        0.04832063                     0.03089251
## 4                        0.07183016                     0.04284108
## 5                        0.06606479                     0.04456762
## 6                        0.05979539                     0.04142017
## 7                        0.06824971                     0.03995093
## 8                        0.06728641                     0.04786895
## 9                        0.05323997                     0.03091972
## 10                       0.05988038                     0.03724856
## 11                       0.06617902                     0.03586795
## 12                       0.04989375                     0.02629529
## 13                       0.08227127                     0.06378930
## 14                       0.06883946                     0.03828356
## 15                       0.07810889                     0.05821137
## 16                       0.05568294                     0.03333882
## 17                       0.06136785                     0.03288086
## 18                       0.07954142                     0.06915887
## 19                       0.05158986                     0.03241119
## 20                       0.06315722                     0.04604265
## 21                       0.14680583                     0.12353011
## 22                       0.08650905                     0.07640071
## 23                       0.08649545                     0.06059171
## 24                       0.07135740                     0.05519514
## 25                       0.06983895                     0.05738763
## 26                       0.07963156                     0.05618883
## 27                       0.08711074                     0.07079550
## 28                       0.06824971                     0.03995093
## 29                       0.06418275                     0.05032447
## 30                       0.05222191                     0.03244346
## 31                       0.07113053                     0.04763499
## 32                       0.05693517                     0.03671770
## 33                       0.06562334                     0.04685533
## 34                       0.06239977                     0.04198460
## 35                       0.05454167                     0.03399002
## 36                       0.07333644                     0.05035574
## 37                       0.07329403                     0.05731750
## 38                       0.07636461                     0.05103995
## 39                       0.10953189                     0.07299194
## 40                       0.08043981                     0.05352156
## 41                       0.07313037                     0.04178375
## 42                       0.07410342                     0.05622075
## 43                       0.06524362                     0.04600758
## 44                       0.10312285                     0.07693306
## 45                       0.05587196                     0.03368962
## 46                       0.06105502                     0.03190629
## 47                       0.06498986                     0.03619874
## 48                       0.07216754                     0.04874046
## 49                       0.08885184                     0.07997795
## 50                       0.06391519                     0.03787766
## 51                       0.06891566                     0.04983750
## 52                       0.09540828                     0.07664528
## 53                       0.05377745                     0.04997813
## 54                       0.06009851                     0.04046064
## 55                       0.06524820                     0.04899315
## 56                       0.05952973                     0.03440993
## 57                       0.05854461                     0.03518064
## 58                       0.06418663                     0.03744168
## 59                       0.07948485                     0.05308449
## 60                       0.12097967                     0.08843957
## 61                       0.08176672                     0.05979096
## 62                       0.10271031                     0.07709501
## 63                       0.05975595                     0.03778847
## 64                       0.10183863                     0.09714995
## 65                       0.06233683                     0.04060192
## 66                       0.04709106                     0.02810443
## 67                       0.05206058                     0.03209720
## 68                       0.06045899                     0.04443489
## 69                       0.13135169                     0.11748524
## 70                       0.06569047                     0.03708798
## 71                       0.07547847                     0.04821869
## 72                       0.05418796                     0.03543144
## 73                       0.08549992                     0.06433801
## 74                       0.06493609                     0.04228524
## 75                       0.08503921                     0.06754292
## 76                       0.07108620                     0.04985370
## 77                       0.05635307                     0.03575308
## 78                       0.07681101                     0.06197821
## 79                       0.05449343                     0.03517051
## 80                       0.07733093                     0.06036908
## 81                       0.08033759                     0.06357934
## 82                       0.06745152                     0.04980979
## 83                       0.06345728                     0.04700534
## 84                       0.08179625                     0.06450658
## 85                       0.13869130                     0.12570487
## 86                       0.07359921                     0.06006352
## 87                       0.06029880                     0.03524766
## 88                       0.06738130                     0.04573442
## 89                       0.05218262                     0.03664799
## 90                       0.07457434                     0.05049869
## 91                       0.14817670                     0.12273592
## 92                       0.08129635                     0.06722978
## 93                       0.04526294                     0.02965194
## 94                       0.07111162                     0.05008626
## 95                       0.04665594                     0.03196119
## 96                       0.05329689                     0.03315169
## 97                       0.07135740                     0.05519514
## 98                       0.10312285                     0.07693306
## 99                       0.06251893                     0.03727646
## 100                      0.10648693                     0.10977560
## 101                      0.04901332                     0.03133030
## 102                      0.05346797                     0.03922608
## 103                      0.05700950                     0.03130454
## 104                      0.05879797                     0.03368153
## 105                      0.05876170                     0.05782005
## 106                      0.08540098                     0.06928271
## 107                      0.05939544                     0.03477889
## 108                      0.07531209                     0.05007817
## 109                      0.09960867                     0.07113439
## 110                      0.08890245                     0.07953257
## 111                      0.05849901                     0.03210397
## 112                      0.08584369                     0.07132728
## 113                      0.06673642                     0.04755361
## 114                      0.06524820                     0.04899315
## 115                      0.07139696                     0.04532466
## 116                      0.07291030                     0.05190282
## 117                      0.07148707                     0.05802342
## 118                      0.05346797                     0.03922608
## 119                      0.05067088                     0.03188933
## 120                      0.06009851                     0.04046064
## 121                      0.06233683                     0.04060192
## 122                      0.06587971                     0.04070586
## 123                      0.05099242                     0.03444683
## 124                      0.05206058                     0.03209720
## 125                      0.10281589                     0.08050321
## 126                      0.07650982                     0.05573459
## 127                      0.05513372                     0.03018383
## 128                      0.06379546                     0.04146396
## 129                      0.06519671                     0.04037309
## 130                      0.06160098                     0.04557137
## 131                      0.05188739                     0.03271461
## 132                      0.06370561                     0.04467488
## 133                      0.08331952                     0.06632276
## 134                      0.04672317                     0.02867385
## 135                      0.07216754                     0.04874046
## 136                      0.06234531                     0.03614920
## 137                      0.06559506                     0.04342078
## 138                      0.07060366                     0.03758621
## 139                      0.07564028                     0.04460858
## 140                      0.06651243                     0.03917281
## 141                      0.06473456                     0.04045008
## 142                      0.08953207                     0.07116069
## 143                      0.06529098                     0.04179676
## 144                      0.05452654                     0.03487479
## 145                      0.05918681                     0.03967870
## 146                      0.05325974                     0.03364415
## 147                      0.07063128                     0.03756827
## 148                      0.08108983                     0.06551311
## 149                      0.07599356                     0.05425326
## 150                      0.06326472                     0.03733489
## 151                      0.07324374                     0.05959721
## 152                      0.07371311                     0.04435108
## 153                      0.07547847                     0.04821869
## 154                      0.06763876                     0.05144766
## 155                      0.07578103                     0.07126250
## 156                      0.06524820                     0.04899315
## 157                      0.07084683                     0.04165900
## 158                      0.07709500                     0.05338011
## 159                      0.06918417                     0.05138435
## 160                      0.07235735                     0.05115666
## 161                      0.09857512                     0.07490039
## 162                      0.07808019                     0.04862327
## 163                      0.06977723                     0.04468004
## 164                      0.10558691                     0.08189807
## 165                      0.06060968                     0.04201091
## 166                      0.08136031                     0.05270174
## 167                      0.04901332                     0.03133030
## 168                      0.09979655                     0.08788981
## 169                      0.05008954                     0.03126459
## 170                      0.09030158                     0.06399238
## 171                      0.06320632                     0.04240118
## 172                      0.05905622                     0.03378478
## 173                      0.07275607                     0.04150129
## 174                      0.06692842                     0.04839782
## 175                      0.10017024                     0.09306215
## 176                      0.05803433                     0.03365074
## 177                      0.05425036                     0.03336004
## 178                      0.09979655                     0.08788981
## 179                      0.06569047                     0.03708798
## 180                      0.07389443                     0.04859544
## 181                      0.05461915                     0.03401871
## 182                      0.06810603                     0.04144163
## 183                      0.10971127                     0.08089051
## 184                      0.08102636                     0.05181958
## 185                      0.07769129                     0.06016798
## 186                      0.06276065                     0.03893518
## 187                      0.08033759                     0.06357934
## 188                      0.08456680                     0.06248878
## 189                      0.07599771                     0.05636149
## 190                      0.05717941                     0.03509052
## 191                      0.06023030                     0.04324281
## 192                      0.05184695                     0.03257326
## 193                      0.05062692                     0.03326498
## 194                      0.05807897                     0.03840399
## 195                      0.07143265                     0.04644875
## 196                      0.05346797                     0.03922608
## 197                      0.08534059                     0.06665553
## 198                      0.05597971                     0.03236934
## 199                      0.10978728                     0.08644671
## 200                      0.07894664                     0.05392020
## 201                      0.07128426                     0.05060916
## 202                      0.06673642                     0.04755361
## 203                      0.05295592                     0.03197682
## 204                      0.06544598                     0.03571049
## 205                      0.10086199                     0.07990320
## 206                      0.06216823                     0.04118072
## 207                      0.05828521                     0.03228211
## 208                      0.07549737                     0.03659976
## 209                      0.06243358                     0.03481118
## 210                      0.05418796                     0.03543144
## 211                      0.05674839                     0.03174640
## 212                      0.07993889                     0.05697609
## 213                      0.06913032                     0.04072278
## 214                      0.07347612                     0.05138541
## 215                      0.10224293                     0.07459458
## 216                      0.06000543                     0.04297320
## 217                      0.05603962                     0.04061396
## 218                      0.05387495                     0.03824942
## 219                      0.06345728                     0.04700534
## 220                      0.05624021                     0.03851551
## 221                      0.06271764                     0.03240188
## 222                      0.06728641                     0.04786895
## 223                      0.06009851                     0.04046064
## 224                      0.07657460                     0.05230753
## 225                      0.05896573                     0.04186849
## 226                      0.08305510                     0.06901819
## 227                      0.07578526                     0.05522518
## 228                      0.06171069                     0.04085533
## 229                      0.07375659                     0.05114495
## 230                      0.06442653                     0.03424683
## 231                      0.05386779                     0.03829098
## 232                      0.05595832                     0.03426186
## 233                      0.06654160                     0.04224341
## 234                      0.08739021                     0.06108798
## 235                      0.08509418                     0.06756728
## 236                      0.07949101                     0.06009125
## 237                      0.06711270                     0.04028321
## 238                      0.06910944                     0.03720729
## 239                      0.06402305                     0.04598828
## 240                      0.06811397                     0.04105829
## 241                      0.05768942                     0.03118525
## 242                      0.07650982                     0.05573459
## 243                      0.05312926                     0.03724206
## 244                      0.06718406                     0.03950498
## 245                      0.08009117                     0.07535422
## 246                      0.06396844                     0.03600987
## 247                      0.08364446                     0.06324277
## 248                      0.06029880                     0.03524766
## 249                      0.07193452                     0.03980235
## 250                      0.05471576                     0.03582247
## 251                      0.07113039                     0.04434575
## 252                      0.08958166                     0.06756876
## 253                      0.07613529                     0.04891227
## 254                      0.05620184                     0.03568303
## 255                      0.10648693                     0.10977560
## 256                      0.07986487                     0.05147147
## 257                      0.07689942                     0.05620251
## 258                      0.06391519                     0.03787766
## 259                      0.06517076                     0.03636705
## 260                      0.10183863                     0.09714995
## 261                      0.05568294                     0.03333882
## 262                      0.06124118                     0.03381654
## 263                      0.06159037                     0.03618107
## 264                      0.05335823                     0.03533580
## 265                      0.05529599                     0.03952869
## 266                      0.07948485                     0.05308449
## 267                      0.10971127                     0.08089051
## 268                      0.10710198                     0.08174284
## 269                      0.08155697                     0.06175339
## 270                      0.05773772                     0.03644037
## 271                      0.05513372                     0.03018383
## 272                      0.05624021                     0.03851551
## 273                      0.04928490                     0.03294182
## 274                      0.09174070                     0.06716748
## 275                      0.09838453                     0.07818091
## 276                      0.06826221                     0.04701206
## 277                      0.06950783                     0.03670310
## 278                      0.07106984                     0.04606575
## 279                      0.05207394                     0.03922154
## 280                      0.06493609                     0.04228524
## 281                      0.05786774                     0.03394946
## 282                      0.06554570                     0.03680992
## 283                      0.06197011                     0.04968730
## 284                      0.06825921                     0.05006180
## 285                      0.08360388                     0.06631620
## 286                      0.07935895                     0.04076070
## 287                      0.05876170                     0.05782005
## 288                      0.05795966                     0.05290020
## 289                      0.07496861                     0.06139906
## 290                      0.06494627                     0.04016656
## 291                      0.05256392                     0.03108783
## 292                      0.04911108                     0.03178002
## 293                      0.04863611                     0.03088649
## 294                      0.07206443                     0.04887762
## 295                      0.07742805                     0.05385317
## 296                      0.05701522                     0.03888110
## 297                      0.06927541                     0.05053540
## 298                      0.06337056                     0.03914502
## 299                      0.08176672                     0.05979096
## 300                      0.07729352                     0.06151708
## 301                      0.06784633                     0.05169293
## 302                      0.06313918                     0.04285304
## 303                      0.05975595                     0.03778847
## 304                      0.06393911                     0.04249492
## 305                      0.06000543                     0.04297320
## 306                      0.08452061                     0.07165776
## 307                      0.06083906                     0.03274669
## 308                      0.08540098                     0.06928271
## 309                      0.06537797                     0.04451080
## 310                      0.07942801                     0.04539969
## 311                      0.06345683                     0.04560113
## 312                      0.09960867                     0.07113439
## 313                      0.06941670                     0.04672314
## 314                      0.11639298                     0.09000425
## 315                      0.06737915                     0.03619600
## 316                      0.06287419                     0.04045622
## 317                      0.06418275                     0.05032447
## 318                      0.05854461                     0.03518064
## 319                      0.07322047                     0.04944766
## 320                      0.06674111                     0.04437009
## 321                      0.06322161                     0.03624544
## 322                      0.08020407                     0.07685915
## 323                      0.05513372                     0.03018383
## 324                      0.05058385                     0.03296993
## 325                      0.05355767                     0.03202474
## 326                      0.05553180                     0.03467101
## 327                      0.06524820                     0.04899315
## 328                      0.05495093                     0.03394418
## 329                      0.07278791                     0.03457902
## 330                      0.08547778                     0.05213322
## 331                      0.06864268                     0.03751104
## 332                      0.07183016                     0.04284108
## 333                      0.06567671                     0.04682501
## 334                      0.06703621                     0.04278393
## 335                      0.05355767                     0.03202474
## 336                      0.08004176                     0.05576572
## 337                      0.05457303                     0.03601836
## 338                      0.06098655                     0.03309991
## 339                      0.06338538                     0.03464497
## 340                      0.08669217                     0.05340195
## 341                      0.08739021                     0.06108798
## 342                      0.05466528                     0.03146900
## 343                      0.17119876                     0.16353552
## 344                      0.06271764                     0.03240188
## 345                      0.06539354                     0.03613134
## 346                      0.08226882                     0.04659242
## 347                      0.08684534                     0.05071583
## 348                      0.05472834                     0.03671645
## 349                      0.06996412                     0.06679460
## 350                      0.07019788                     0.03806895
## 351                      0.07742968                     0.06762071
## 352                      0.06000543                     0.04297320
## 353                      0.05858076                     0.03223953
## 354                      0.05325974                     0.03364415
## 355                      0.05000828                     0.02778772
## 356                      0.05396156                     0.03272421
## 357                      0.05795966                     0.05290020
## 358                      0.05563324                     0.03014288
## 359                      0.05186385                     0.03627590
## 360                      0.05355767                     0.03202474
## 361                      0.06837475                     0.04409540
## 362                      0.08584369                     0.07132728
## 363                      0.06711270                     0.04028321
## 364                      0.06811397                     0.04105829
## 365                      0.07987765                     0.04603791
## 366                      0.06008343                     0.04439445
## 367                      0.06966073                     0.05879086
## 368                      0.05562376                     0.03271656
## 369                      0.04906827                     0.03494947
## 370                      0.05421985                     0.03419876
## 371                      0.05593641                     0.03529369
## 372                      0.07106984                     0.04606575
## 373                      0.06200162                     0.03875931
## 374                      0.05387495                     0.03824942
## 375                      0.05058112                     0.03483657
## 376                      0.08472126                     0.06538954
## 377                      0.06667016                     0.03691152
## 378                      0.05499596                     0.03332966
## 379                      0.06253860                     0.04034013
## 380                      0.07104965                     0.07031289
## 381                      0.07145294                     0.04970323
## 382                      0.07526647                     0.04436964
## 383                      0.14635984                     0.12989555
## 384                      0.07063128                     0.03756827
## 385                      0.08485865                     0.04845876
## 386                      0.06819403                     0.03704615
## 387                      0.11095967                     0.10372218
## 388                      0.09346865                     0.09038556
## 389                      0.06243358                     0.03481118
## 390                      0.07548740                     0.04565927
## 391                      0.05874088                     0.03445576
## 392                      0.06412673                     0.04071659
## 393                      0.06711270                     0.04028321
## 394                      0.05768411                     0.03318350
## 395                      0.08589515                     0.06428037
## 396                      0.06251893                     0.03727646
## 397                      0.05520236                     0.03547096
## 398                      0.06445283                     0.03626179
## 399                      0.07686046                     0.05233469
## 400                      0.06826221                     0.04701206
## 401                      0.08206245                     0.06450134
## 402                      0.07686046                     0.05233469
## 403                      0.08930472                     0.08022405
## 404                      0.06370334                     0.03773953
## 405                      0.07333644                     0.05035574
## 406                      0.05971424                     0.04667394
## 407                      0.05733570                     0.03362760
## 408                      0.05932217                     0.03469404
## 409                      0.07102344                     0.04478773
## 410                      0.07347612                     0.05138541
## 411                      0.07731954                     0.04131676
## 412                      0.06042194                     0.03934732
## 413                      0.06365268                     0.03705146
## 414                      0.06786701                     0.04178400
## 415                      0.05592162                     0.04660945
## 416                      0.08945258                     0.06536024
## 417                      0.07589251                     0.04646515
## 418                      0.11088639                     0.07370502
## 419                      0.05999314                     0.03570408
## 420                      0.05928100                     0.03311537
## 421                      0.08235890                     0.05228865
## 422                      0.06477475                     0.04426906
## 423                      0.07389443                     0.04859544
## 424                      0.05595236                     0.02968202
## 425                      0.05058385                     0.03296993
## 426                      0.05388149                     0.03017975
## 427                      0.05752615                     0.03225089
## 428                      0.05880137                     0.03712406
## 429                      0.07373740                     0.04814434
## 430                      0.08280872                     0.04877597
## 431                      0.04867487                     0.03101102
## 432                      0.06313201                     0.04637740
## 433                      0.08102636                     0.05181958
## 434                      0.06294350                     0.04057094
## 435                      0.06811397                     0.04105829
## 436                      0.11473369                     0.07823683
## 437                      0.06689773                     0.03559766
## 438                      0.05436765                     0.03751046
## 439                      0.06243358                     0.03481118
## 440                      0.04930572                     0.03073425
## 441                      0.06105502                     0.03190629
## 442                      0.05247787                     0.02908197
## 443                      0.05874088                     0.03445576
## 444                      0.05874088                     0.03445576
## 445                      0.05528231                     0.03882773
## 446                      0.04948365                     0.03336420
## 447                      0.07913761                     0.07253301
## 448                      0.06747200                     0.03949776
## 449                      0.06515902                     0.03579813
## 450                      0.06651243                     0.03917281
## 451                      0.05335823                     0.03533580
## 452                      0.09163493                     0.08113126
## 453                      0.05874088                     0.03445576
## 454                      0.09662308                     0.09116419
## 455                      0.05099242                     0.03444683
## 456                      0.07375296                     0.05618030
## 457                      0.05607607                     0.03348497
## 458                      0.05436765                     0.03751046
## 459                      0.05595832                     0.03426186
## 460                      0.06243358                     0.03481118
## 461                      0.06560774                     0.03710307
## 462                      0.05709970                     0.03230226
## 463                      0.05454834                     0.03800748
## 464                      0.06739723                     0.05027260
## 465                      0.11159153                     0.09991319
## 466                      0.07628028                     0.03967315
## 467                      0.08344452                     0.04021579
## 468                      0.05988038                     0.03724856
## 469                      0.05158986                     0.03241119
## 470                      0.06373711                     0.03944403
## 471                      0.08452061                     0.07165776
## 472                      0.05717941                     0.03509052
## 473                      0.05595832                     0.03426186
## 474                      0.05897279                     0.04271294
## 475                      0.05510716                     0.03465839
## 476                      0.04672317                     0.02867385
## 477                      0.07619179                     0.04780933
## 478                      0.10183863                     0.09714995
## 479                      0.05126864                     0.03318395
## 480                      0.05006946                     0.03443331
## 481                      0.05396156                     0.03272421
## 482                      0.05849901                     0.03210397
## 483                      0.05495093                     0.03394418
## 484                      0.06101091                     0.03658090
## 485                      0.05267443                     0.03454201
## 486                      0.06442653                     0.03424683
## 487                      0.05620184                     0.03568303
## 488                      0.06000543                     0.04297320
## 489                      0.06316116                     0.04319814
## 490                      0.05971921                     0.04195552
## 491                      0.05014005                     0.03338790
## 492                      0.05660060                     0.03168982
## 493                      0.05874088                     0.03445576
## 494                      0.06151229                     0.04069523
## 495                      0.06477968                     0.03501870
## 496                      0.05741756                     0.03589703
## 497                      0.05665650                     0.03108770
## 498                      0.07340700                     0.04362970
## 499                      0.07034321                     0.04915982
## 500                      0.05709970                     0.03230226
## 501                      0.06868180                     0.03852030
## 502                      0.05454167                     0.03399002
## 503                      0.06273746                     0.03853206
## 504                      0.06322231                     0.04234862
## 505                      0.05952973                     0.03440993
## 506                      0.05860859                     0.03750554
## 507                      0.05947651                     0.03638647
## 508                      0.06316116                     0.04319814
## 509                      0.06182222                     0.03885558
## 510                      0.05700950                     0.03130454
## 511                      0.05700950                     0.03130454
## 512                      0.05768942                     0.03118525
## 513                      0.07359921                     0.06006352
## 514                      0.05021059                     0.02991752
## 515                      0.05222191                     0.03244346
## 516                      0.07648542                     0.05183561
## 517                      0.06855732                     0.03492125
## 518                      0.05242846                     0.03290419
## 519                      0.06703621                     0.04278393
## 520                      0.06560774                     0.03710307
## 521                      0.05538966                     0.03122177
## 522                      0.06145551                     0.03289339
## 523                      0.06309889                     0.04879669
## 524                      0.05258992                     0.03288167
## 525                      0.05593641                     0.03529369
## 526                      0.05952981                     0.03627064
## 527                      0.06958370                     0.04119121
## 528                      0.06537241                     0.03474698
## 529                      0.05999314                     0.03570408
## 530                      0.10138579                     0.09608346
## 531                      0.06652126                     0.04555611
## 532                      0.04665594                     0.03196119
## 533                      0.06258489                     0.04405781
## 534                      0.07812902                     0.03942988
## 535                      0.05449343                     0.03517051
## 536                      0.05407116                     0.03557570
## 537                      0.06456722                     0.04421753
## 538                      0.06400930                     0.04153419
## 539                      0.06102778                     0.03646340
## 540                      0.09714962                     0.07502252
## 541                      0.06326472                     0.03733489
## 542                      0.06338538                     0.03464497
## 543                      0.08141415                     0.06484782
## 544                      0.05882807                     0.03062741
## 545                      0.07206443                     0.04887762
## 546                      0.08180540                     0.04542525
## 547                      0.06251841                     0.03561882
## 548                      0.05625517                     0.03622188
## 549                      0.05009693                     0.03037999
## 550                      0.05154420                     0.02802117
## 551                      0.06477602                     0.04456287
## 552                      0.06243358                     0.03481118
## 553                      0.05379800                     0.03301063
## 554                      0.07451170                     0.05566746
## 555                      0.05208125                     0.03209939
## 556                      0.05935570                     0.03502136
## 557                      0.05690321                     0.03497164
## 558                      0.06647786                     0.04189059
## 559                      0.06182222                     0.03885558
## 560                      0.08242338                     0.06545708
## 561                      0.05501931                     0.03240280
## 562                      0.06106690                     0.03278546
## 563                      0.07613529                     0.04891227
## 564                      0.06418663                     0.03744168
## 565                      0.06445283                     0.03626179
## 566                      0.05889548                     0.03589933
## 567                      0.07634688                     0.03969011
## 568                      0.11639298                     0.09000425
## 569                      0.06223053                     0.03981818
## 570                      0.08180540                     0.04542525
## 571                      0.06316116                     0.04319814
## 572                      0.05836956                     0.03448727
## 573                      0.05709970                     0.03230226
## 574                      0.06477475                     0.04426906
## 575                      0.06766923                     0.04273019
## 576                      0.05858933                     0.03285602
## 577                      0.06182222                     0.03885558
## 578                      0.07438354                     0.04951592
## 579                      0.06517076                     0.03636705
## 580                      0.08120280                     0.05664922
## 581                      0.06682774                     0.03668346
## 582                      0.05755088                     0.03506741
## 583                      0.08589515                     0.06428037
## 584                      0.05947745                     0.04450771
## 585                      0.06100341                     0.03553684
## 586                      0.05154420                     0.02802117
## 587                      0.06101091                     0.03658090
## 588                      0.06330136                     0.03711074
## 589                      0.05849901                     0.03210397
## 590                      0.05836956                     0.03448727
## 591                      0.07483649                     0.04197152
## 592                      0.05386779                     0.03829098
## 593                      0.05587196                     0.03368962
## 594                      0.08462372                     0.07756969
## 595                      0.06806946                     0.04035883
## 596                      0.05351282                     0.03373679
## 597                      0.06460147                     0.03317032
## 598                      0.06910944                     0.03720729
## 599                      0.06193317                     0.03461077
## 600                      0.08449860                     0.05440842
## 601                      0.05999314                     0.03570408
## 602                      0.05674429                     0.03482726
## 603                      0.13869130                     0.12570487
## 604                      0.07549737                     0.03659976
## 605                      0.10312285                     0.07693306
## 606                      0.05258992                     0.03288167
## 607                      0.05120110                     0.03322776
## 608                      0.05224583                     0.03455291
## 609                      0.05533427                     0.03348230
## 610                      0.04859882                     0.02971535
## 611                      0.06811397                     0.04105829
## 612                      0.05755088                     0.03506741
## 613                      0.05529599                     0.03952869
## 614                      0.06399081                     0.03713871
## 615                      0.06322161                     0.03624544
## 616                      0.05905622                     0.03378478
## 617                      0.04849251                     0.02999538
## 618                      0.05260395                     0.03191335
## 619                      0.05249960                     0.03240861
## 620                      0.06159037                     0.03618107
## 621                      0.06284052                     0.04471523
## 622                      0.05388392                     0.03352087
## 623                      0.06418663                     0.03744168
## 624                      0.06810603                     0.04144163
## 625                      0.05256392                     0.03108783
## 626                      0.05686890                     0.04294763
## 627                      0.05154420                     0.02802117
## 628                      0.07564028                     0.04460858
## 629                      0.05592162                     0.04660945
## 630                      0.05587196                     0.03368962
## 631                      0.06370233                     0.03908059
## 632                      0.06050273                     0.03638520
## 633                      0.05709970                     0.03230226
## 634                      0.05709970                     0.03230226
## 635                      0.05709970                     0.03230226
## 636                      0.05095559                     0.03227350
## 637                      0.04901332                     0.03133030
## 638                      0.05700950                     0.03130454
## 639                      0.06406298                     0.04626844
## 640                      0.05190822                     0.02973883
## 641                      0.05882807                     0.03062741
## 642                      0.06971374                     0.05060080
## 643                      0.06894852                     0.04033718
## 644                      0.06586464                     0.03550045
## 645                      0.06667016                     0.03691152
## 646                      0.09672613                     0.08468098
## 647                      0.05733570                     0.03362760
## 648                      0.04948365                     0.03336420
## 649                      0.07729352                     0.06151708
## 650                      0.06368023                     0.03897369
## 651                      0.05711879                     0.03506771
## 652                      0.06107760                     0.04274052
## 653                      0.05709970                     0.03230226
## 654                      0.05425036                     0.03336004
## 655                      0.05999314                     0.03570408
## 656                      0.06520045                     0.03803596
## 657                      0.05386860                     0.03826233
## 658                      0.07800718                     0.04187074
## 659                      0.06316116                     0.04319814
## 660                      0.05014005                     0.03338790
## 661                      0.05328669                     0.03497358
## 662                      0.07987765                     0.04603791
## 663                      0.07056838                     0.05074401
## 664                      0.05388392                     0.03352087
## 665                      0.05587196                     0.03368962
## 666                      0.05900420                     0.03433363
## 667                      0.05874088                     0.03445576
## 668                      0.06216823                     0.04118072
## 669                      0.05549232                     0.03244551
## 670                      0.05289130                     0.03025847
## 671                      0.05058112                     0.03483657
## 672                      0.06658851                     0.03735758
## 673                      0.12702950                     0.11742063
## 674                      0.07548740                     0.04565927
## 675                      0.05828521                     0.03228211
## 676                      0.05568294                     0.03333882
## 677                      0.06711270                     0.04028321
## 678                      0.04665594                     0.03196119
## 679                      0.05123059                     0.03039872
## 680                      0.06289103                     0.03327960
## 681                      0.06617902                     0.03586795
## 682                      0.07019788                     0.03806895
## 683                      0.06154949                     0.03373265
## 684                      0.05967322                     0.03454763
## 685                      0.05675535                     0.03410946
## 686                      0.05969329                     0.03287838
## 687                      0.04901332                     0.03133030
## 688                      0.05217510                     0.03313153
## 689                      0.06200162                     0.03875931
## 690                      0.08136031                     0.05270174
## 691                      0.06271764                     0.03240188
## 692                      0.06732775                     0.04401836
## 693                      0.05123059                     0.03039872
## 694                      0.06705819                     0.03640339
## 695                      0.06462719                     0.03648455
## 696                      0.06586464                     0.03550045
## 697                      0.06843461                     0.04072220
## 698                      0.06316116                     0.04319814
## 699                      0.05755088                     0.03506741
## 700                      0.04948365                     0.03336420
## 701                      0.05755088                     0.03506741
## 702                      0.06289103                     0.03327960
## 703                      0.05674839                     0.03174640
## 704                      0.05775148                     0.03369621
## 705                      0.06544598                     0.03571049
## 706                      0.06232660                     0.03707266
## 707                      0.08830528                     0.06336534
## 708                      0.05154420                     0.02802117
## 709                      0.04866190                     0.03040967
## 710                      0.06178796                     0.03711028
## 711                      0.06868180                     0.03852030
## 712                      0.05095559                     0.03227350
## 713                      0.06251893                     0.03727646
## 714                      0.14571952                     0.12123729
## 715                      0.06910944                     0.03720729
## 716                      0.05999314                     0.03570408
## 717                      0.05258992                     0.03288167
## 718                      0.05824597                     0.03149340
## 719                      0.05733897                     0.03120292
## 720                      0.06159037                     0.03618107
## 721                      0.05858933                     0.03285602
## 722                      0.06243172                     0.03336454
## 723                      0.05501931                     0.03240280
## 724                      0.04849251                     0.02999538
## 725                      0.06410157                     0.03708863
## 726                      0.06971374                     0.05060080
## 727                      0.07366898                     0.03838932
## 728                      0.05388392                     0.03352087
## 729                      0.05967322                     0.03454763
## 730                      0.05907829                     0.03278308
## 731                      0.06176147                     0.03338262
## 732                      0.05768942                     0.03118525
## 733                      0.06212900                     0.03362169
## 734                      0.07613276                     0.05951164
## 735                      0.04827910                     0.03023868
## 736                      0.06971374                     0.05060080
## 737                      0.08180540                     0.04542525
## 738                      0.07019788                     0.03806895
## 739                      0.06290700                     0.04003230
## 740                      0.05126864                     0.03318395
## 741                      0.06766923                     0.04273019
## 742                      0.06523415                     0.03543773
## 743                      0.05267443                     0.03454201
## 744                      0.04859882                     0.02971535
## 745                      0.06586464                     0.03550045
## 746                      0.05474087                     0.03258930
## 747                      0.04966999                     0.03171713
## 748                      0.05242846                     0.03290419
## 749                      0.04867487                     0.03101102
## 750                      0.06605538                     0.03714686
## 751                      0.06316116                     0.04319814
## 752                      0.05684347                     0.03258546
## 753                      0.05021059                     0.02991752
## 754                      0.07060366                     0.03758621
## 755                      0.07812902                     0.03942988
## 756                      0.04948365                     0.03336420
## 757                      0.06040228                     0.03338796
## 758                      0.05367073                     0.03131338
## 759                      0.05674839                     0.03174640
## 760                      0.05709970                     0.03230226
## 761                      0.06855732                     0.03492125
## 762                      0.05896573                     0.04186849
## 763                      0.05258992                     0.03288167
## 764                      0.05123059                     0.03039872
## 765                      0.04963325                     0.03043224
## 766                      0.06438035                     0.03670436
## 767                      0.05067088                     0.03188933
## 768                      0.05067088                     0.03188933
## 769                      0.06523415                     0.03543773
## 770                      0.05665650                     0.03108770
## 771                      0.05256392                     0.03108783
## 772                      0.05549232                     0.03244551
## 773                      0.06406298                     0.04626844
## 774                      0.05715872                     0.03155801
## 775                      0.05250631                     0.03206428
## 776                      0.05274492                     0.03230868
## 777                      0.05067088                     0.03188933
## 778                      0.06145551                     0.03289339
## 779                      0.05377108                     0.03488120
## 780                      0.04948365                     0.03336420
## 781                      0.05900420                     0.03433363
## 782                      0.06330467                     0.03955250
## 783                      0.05907829                     0.03278308
## 784                      0.06045442                     0.03391513
## 785                      0.05067088                     0.03188933
## 786                      0.05258992                     0.03288167
## 787                      0.05810604                     0.03227261
## 788                      0.06808002                     0.03413730
## 789                      0.06855732                     0.03492125
## 790                      0.05293965                     0.03205740
## 791                      0.05067088                     0.03188933
## 792                      0.05660060                     0.03168982
## 793                      0.05768942                     0.03118525
## 794                      0.05139349                     0.03108955
## 795                      0.05810604                     0.03227261
## 796                      0.05783549                     0.03562709
## 797                      0.05907829                     0.03278308
## 798                      0.05810604                     0.03227261
## 799                      0.05709970                     0.03230226
## 800                      0.06189760                     0.03566208
## 801                      0.05981702                     0.03439278
## 802                      0.04948365                     0.03336420
## 803                      0.05881047                     0.03367400
## 804                      0.05969329                     0.03287838
## 805                      0.05807867                     0.03270711
## 806                      0.05258992                     0.03288167
## 807                      0.05968998                     0.03420008
## 808                      0.05871587                     0.03585085
## 809                      0.06212900                     0.03362169
## 810                      0.05952973                     0.03440993
## 811                      0.05968998                     0.03420008
## 812                      0.05810604                     0.03227261
## 813                      0.05014005                     0.03338790
##     posterior_median_clay_skill_winner posterior_median_grass_skill_winner
## 1                         -0.106535000                         0.085743150
## 2                         -0.080121780                        -0.059804775
## 3                          0.121787300                         0.228918600
## 4                          0.043265900                         0.207529180
## 5                          0.134906150                         0.020843115
## 6                         -0.231992050                         0.061152160
## 7                          0.296374700                         0.231212845
## 8                          0.094539400                         0.038592300
## 9                          0.099612360                         0.144866425
## 10                         0.154120300                         0.206060450
## 11                         0.568133000                         0.284546000
## 12                         0.587975500                         0.340471300
## 13                        -0.022833000                        -0.078050200
## 14                         0.543806000                         0.266882000
## 15                        -0.026171700                        -0.056532930
## 16                         0.225343650                         0.184115100
## 17                         0.367714100                         0.204019000
## 18                         0.139282200                        -0.027111790
## 19                         0.324960705                         0.354993550
## 20                        -0.056673750                         0.072115385
## 21                         0.026596005                        -0.104232350
## 22                        -0.027245350                        -0.098154165
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## 472                       -0.086789900                         0.156895550
## 473                        0.188669950                         0.229737210
## 474                       -0.060662300                         0.169191800
## 475                        0.367405500                         0.138614950
## 476                        0.376239500                         0.365091950
## 477                        0.241011600                         0.057900750
## 478                       -0.026755760                         0.068709000
## 479                        0.486528800                         0.555446300
## 480                        0.149357550                         0.096047300
## 481                        0.147790700                         0.112836850
## 482                        0.215546650                         0.182321500
## 483                        0.074227000                         0.201856650
## 484                        0.366366950                         0.225881050
## 485                        0.227446350                         0.226185085
## 486                        0.178045915                         0.177698500
## 487                        0.176873000                         0.147508115
## 488                       -0.230546650                         0.072643400
## 489                        0.326519500                         0.135869950
## 490                       -0.097657650                         0.097327150
## 491                        0.487750400                         0.556291300
## 492                        0.427764900                         0.350401300
## 493                        0.160583950                         0.114714800
## 494                       -0.225076000                         0.070483350
## 495                        0.329244800                         0.272394900
## 496                        0.358617000                         0.137035800
## 497                        0.306405925                         0.282253500
## 498                        0.228395550                         0.038335200
## 499                        0.147720965                        -0.066578200
## 500                        0.880221500                         0.452966500
## 501                        0.319815200                         0.241829850
## 502                        0.148891790                         0.146446800
## 503                        0.319133550                         0.121636250
## 504                        0.015702500                         0.136205250
## 505                        0.565891850                         0.546195450
## 506                        0.160217800                         0.133677160
## 507                        0.106477000                         0.212003350
## 508                        0.326519500                         0.135869950
## 509                        0.039858200                         0.210476165
## 510                        0.070880500                         0.217460200
## 511                        0.070880500                         0.217460200
## 512                        0.885219500                         0.452808000
## 513                        0.142237500                         0.212791200
## 514                        0.666664885                         0.583749000
## 515                        0.143534400                         0.115953650
## 516                        0.121810850                        -0.035570270
## 517                        0.915445000                         0.446478500
## 518                        0.488083150                         0.556654700
## 519                        0.132175045                         0.018083205
## 520                        0.202694600                         0.101902665
## 521                        0.218109700                         0.177524050
## 522                        0.659370829                         0.522014000
## 523                        0.095604450                         0.121349100
## 524                        0.488397700                         0.552261100
## 525                        0.186276500                         0.226958750
## 526                        0.359708000                         0.135557350
## 527                        0.251856600                         0.079164200
## 528                        0.415446920                         0.357736150
## 529                        0.484295000                         0.536037200
## 530                       -0.028804900                         0.068372750
## 531                        0.122102150                         0.017909825
## 532                        0.458449900                         0.578017050
## 533                       -0.101391300                         0.097446135
## 534                        0.319573250                         0.248107850
## 535                        0.187747550                         0.227113450
## 536                        0.228443395                         0.218096700
## 537                       -0.054586800                         0.155356700
## 538                       -0.080349850                         0.057655050
## 539                        0.221231470                         0.184121700
## 540                        0.145843600                        -0.017761020
## 541                        0.134176750                         0.127811500
## 542                        0.245484250                         0.236135030
## 543                        0.111357850                         0.021392545
## 544                        0.333070335                         0.297296350
## 545                       -0.162944500                         0.077918450
## 546                        0.327104700                         0.112656350
## 547                        0.220249865                         0.177426550
## 548                        0.159437300                         0.127420600
## 549                        0.586153000                         0.349648650
## 550                        0.413021595                         0.374015950
## 551                       -0.072943200                         0.045631685
## 552                        0.371700750                         0.203966200
## 553                        0.183185400                         0.227310800
## 554                        0.042697600                        -0.042982900
## 555                        0.314839250                         0.280839250
## 556                        0.585093100                         0.537030600
## 557                        0.162447800                         0.118545950
## 558                        0.254525450                         0.250172200
## 559                        0.039858200                         0.210476165
## 560                        0.044142200                         0.022037575
## 561                        0.568594500                         0.360643250
## 562                        0.873091500                         0.452545900
## 563                        0.103297650                         0.047058050
## 564                        0.044238000                         0.204724395
## 565                        0.035034000                         0.060287500
## 566                        0.361582000                         0.132772200
## 567                        0.372579400                         0.210603850
## 568                        0.050208065                        -0.105951325
## 569                        0.116950500                         0.236690900
## 570                        0.327104700                         0.112656350
## 571                        0.326519500                         0.135869950
## 572                        0.373497050                         0.232372700
## 573                        0.880221500                         0.452966500
## 574                       -0.103058850                         0.102546000
## 575                        0.321433000                         0.142747735
## 576                        0.317365300                         0.281169100
## 577                        0.039858200                         0.210476165
## 578                        0.034120165                         0.035237550
## 579                        0.312590400                         0.247405000
## 580                       -0.019655600                         0.030571215
## 581                        0.123948500                         0.211699500
## 582                        0.585332500                         0.350563750
## 583                        0.159870400                         0.180367700
## 584                        0.068208750                        -0.061682800
## 585                       -0.106416750                         0.100165330
## 586                        0.413021595                         0.374015950
## 587                        0.366366950                         0.225881050
## 588                        0.328330150                         0.262840900
## 589                        0.215546650                         0.182321500
## 590                        0.373497050                         0.232372700
## 591                       -0.072225500                         0.255905050
## 592                        0.037256000                         0.134748515
## 593                        0.586383500                         0.350993300
## 594                        0.024384880                        -0.055844900
## 595                        0.168530350                         0.026961550
## 596                        0.128486250                         0.188008300
## 597                        0.314540000                         0.364504005
## 598                        0.382805350                         0.209797700
## 599                        0.366258000                         0.207507500
## 600                        0.053619000                        -0.253238050
## 601                        0.484295000                         0.536037200
## 602                        0.228546114                         0.191616300
## 603                        0.132421250                         0.029175200
## 604                        0.375258600                         0.219416950
## 605                        0.146020000                        -0.023882525
## 606                        0.488397700                         0.552261100
## 607                        0.490366950                         0.560320250
## 608                        0.120527500                         0.247894500
## 609                        0.210305505                         0.216183510
## 610                        0.580894000                         0.347283300
## 611                        0.097696000                         0.206691850
## 612                        0.585332500                         0.350563750
## 613                        0.167536600                         0.063413850
## 614                        0.328522100                         0.259925550
## 615                        0.337881850                         0.227910200
## 616                        0.097043000                         0.213057700
## 617                        0.377990570                         0.366306350
## 618                        0.227268885                         0.221781650
## 619                        0.332389950                         0.234957150
## 620                        0.234502600                         0.184307350
## 621                       -0.071657600                         0.046999450
## 622                        0.581806450                         0.567560500
## 623                        0.044238000                         0.204724395
## 624                        0.311534750                         0.135420150
## 625                        0.306884700                         0.311800850
## 626                        0.186574800                         0.127511350
## 627                        0.413021595                         0.374015950
## 628                        0.134667200                         0.118204130
## 629                        0.185485950                         0.289195450
## 630                        0.586383500                         0.350993300
## 631                        0.044169000                         0.211514450
## 632                        0.144650450                         0.144342650
## 633                        0.880221500                         0.452966500
## 634                        0.880221500                         0.452966500
## 635                        0.880221500                         0.452966500
## 636                        0.596452700                         0.560271000
## 637                        0.355497255                         0.356507350
## 638                        0.070880500                         0.217460200
## 639                        0.105674050                         0.022836550
## 640                        0.374552375                         0.356718260
## 641                        0.333070335                         0.297296350
## 642                        0.157556300                         0.192789200
## 643                        0.338105450                         0.064482100
## 644                        0.581881000                         0.284093000
## 645                        0.222314800                         0.192088700
## 646                       -0.037341600                         0.010573100
## 647                        0.314612550                         0.279132900
## 648                        0.587333350                         0.558021200
## 649                        0.129525150                        -0.075214050
## 650                        0.158311450                         0.141791850
## 651                        0.359103000                         0.139323750
## 652                        0.090328500                         0.017528850
## 653                        0.880221500                         0.452966500
## 654                        0.191090150                         0.157252100
## 655                        0.484295000                         0.536037200
## 656                        0.335796000                         0.233565250
## 657                       -0.054686075                         0.140574500
## 658                        0.189165250                         0.028131750
## 659                        0.326519500                         0.135869950
## 660                        0.487750400                         0.556291300
## 661                        0.226139600                         0.222911350
## 662                        0.315701350                         0.088989050
## 663                        0.218368200                         0.185912815
## 664                        0.581806450                         0.567560500
## 665                        0.586383500                         0.350993300
## 666                        0.371669300                         0.201003750
## 667                        0.160583950                         0.114714800
## 668                        0.112322500                         0.241731500
## 669                        0.426682760                         0.345976650
## 670                        0.405615250                         0.359612350
## 671                        0.148399050                         0.101856135
## 672                        0.172364150                         0.199682450
## 673                       -0.231810500                        -0.217176550
## 674                        0.246288800                         0.049983600
## 675                        0.587158500                         0.350212700
## 676                        0.225343650                         0.184115100
## 677                        0.320669650                         0.137588700
## 678                        0.458449900                         0.578017050
## 679                        0.305121100                         0.312099900
## 680                        0.245897470                         0.225517800
## 681                        0.568133000                         0.284546000
## 682                        0.384851950                         0.205321000
## 683                        0.251893950                         0.232978600
## 684                        0.370903100                         0.207742200
## 685                        0.159579955                         0.118423000
## 686                        0.893176000                         0.451411950
## 687                        0.355497255                         0.356507350
## 688                        0.142490935                         0.112436450
## 689                        0.322034400                         0.246491150
## 690                        0.039300000                        -0.251493200
## 691                        0.337107600                         0.285427750
## 692                        0.250085500                         0.068647380
## 693                        0.305121100                         0.312099900
## 694                        0.551180500                         0.280882000
## 695                        0.568741300                         0.276819500
## 696                        0.581881000                         0.284093000
## 697                        0.146657950                         0.143274200
## 698                        0.326519500                         0.135869950
## 699                        0.585332500                         0.350563750
## 700                        0.587333350                         0.558021200
## 701                        0.585332500                         0.350563750
## 702                        0.245897470                         0.225517800
## 703                        0.587694000                         0.357857150
## 704                        0.370493600                         0.203078600
## 705                        0.171162800                         0.108660600
## 706                        0.204628450                         0.101916050
## 707                        0.023378850                         0.020633350
## 708                        0.413021595                         0.374015950
## 709                        0.583688400                         0.555515950
## 710                        0.229840645                         0.185360450
## 711                        0.319815200                         0.241829850
## 712                        0.596452700                         0.560271000
## 713                        0.025990500                         0.206456100
## 714                        0.163181100                         0.037172450
## 715                        0.382805350                         0.209797700
## 716                        0.484295000                         0.536037200
## 717                        0.488397700                         0.552261100
## 718                        0.427813800                         0.356573675
## 719                        0.255704450                         0.251313925
## 720                        0.234502600                         0.184307350
## 721                        0.317365300                         0.281169100
## 722                        0.326331400                         0.279368450
## 723                        0.568594500                         0.360643250
## 724                        0.377990570                         0.366306350
## 725                        0.175962100                         0.192482350
## 726                        0.157556300                         0.192789200
## 727                        0.334118310                         0.224987000
## 728                        0.581806450                         0.567560500
## 729                        0.370903100                         0.207742200
## 730                        0.880523500                         0.449404500
## 731                        0.567605800                         0.548389600
## 732                        0.885219500                         0.452808000
## 733                        0.916696500                         0.452684050
## 734                        0.158134300                        -0.033180950
## 735                        0.552143400                         0.567512000
## 736                        0.157556300                         0.192789200
## 737                        0.327104700                         0.112656350
## 738                        0.384851950                         0.205321000
## 739                        0.337440240                         0.223071650
## 740                        0.486528800                         0.555446300
## 741                        0.321433000                         0.142747735
## 742                        0.327180500                         0.267886050
## 743                        0.227446350                         0.226185085
## 744                        0.580894000                         0.347283300
## 745                        0.581881000                         0.284093000
## 746                        0.661874850                         0.543734000
## 747                        0.590402050                         0.556577100
## 748                        0.488083150                         0.556654700
## 749                        0.585015450                         0.557569000
## 750                        0.186943950                         0.237784976
## 751                        0.326519500                         0.135869950
## 752                        0.874344500                         0.438915500
## 753                        0.666664885                         0.583749000
## 754                        0.390122800                         0.194635500
## 755                        0.319573250                         0.248107850
## 756                        0.587333350                         0.558021200
## 757                        0.920222000                         0.451721000
## 758                        0.667384350                         0.564973500
## 759                        0.587694000                         0.357857150
## 760                        0.880221500                         0.452966500
## 761                        0.915445000                         0.446478500
## 762                        0.161207400                         0.053490830
## 763                        0.488397700                         0.552261100
## 764                        0.305121100                         0.312099900
## 765                        0.584381000                         0.344768200
## 766                        0.188955100                         0.232708500
## 767                        0.590452100                         0.551250550
## 768                        0.590452100                         0.551250550
## 769                        0.327180500                         0.267886050
## 770                        0.306405925                         0.282253500
## 771                        0.306884700                         0.311800850
## 772                        0.426682760                         0.345976650
## 773                        0.105674050                         0.022836550
## 774                        0.178926950                         0.195880500
## 775                        0.666393650                         0.559337500
## 776                        0.663721350                         0.561039500
## 777                        0.590452100                         0.551250550
## 778                        0.659370829                         0.522014000
## 779                        0.584271500                         0.333582550
## 780                        0.587333350                         0.558021200
## 781                        0.371669300                         0.201003750
## 782                        0.259237350                         0.266646450
## 783                        0.880523500                         0.449404500
## 784                        0.480885000                         0.537228100
## 785                        0.590452100                         0.551250550
## 786                        0.488397700                         0.552261100
## 787                        0.874144000                         0.438578500
## 788                        0.862376000                         0.436440750
## 789                        0.915445000                         0.446478500
## 790                        0.321426750                         0.356651665
## 791                        0.590452100                         0.551250550
## 792                        0.427764900                         0.350401300
## 793                        0.885219500                         0.452808000
## 794                        0.661776900                         0.571112900
## 795                        0.874144000                         0.438578500
## 796                        0.359254300                         0.238361250
## 797                        0.880523500                         0.449404500
## 798                        0.874144000                         0.438578500
## 799                        0.880221500                         0.452966500
## 800                        0.483994500                         0.536794950
## 801                        0.663358500                         0.526354600
## 802                        0.587333350                         0.558021200
## 803                        0.893748000                         0.457424500
## 804                        0.893176000                         0.451411950
## 805                        0.421709650                         0.347388200
## 806                        0.488397700                         0.552261100
## 807                        0.916601000                         0.454273900
## 808                        0.478548500                         0.535242100
## 809                        0.916696500                         0.452684050
## 810                        0.565891850                         0.546195450
## 811                        0.916601000                         0.454273900
## 812                        0.874144000                         0.438578500
## 813                        0.487750400                         0.556291300
##     posterior_median_hard_skill_winner lower.025_q_clay_skill_winner
## 1                          0.067912600                  -0.241222655
## 2                         -0.081090200                  -0.259226000
## 3                          0.200666000                   0.025191725
## 4                          0.169444000                  -0.088733400
## 5                          0.013306000                   0.020455022
## 6                         -0.008307310                  -0.399798791
## 7                          0.285212000                   0.192277475
## 8                          0.051225300                  -0.008830160
## 9                          0.138503500                   0.018644325
## 10                         0.220209500                   0.037503375
## 11                         0.404430000                   0.480990300
## 12                         0.413571000                   0.525671895
## 13                        -0.080525950                  -0.220126200
## 14                         0.383133500                   0.448681098
## 15                        -0.083508500                  -0.149285995
## 16                         0.246287000                   0.136201925
## 17                         0.321332000                   0.282630130
## 18                        -0.006528645                   0.032501149
## 19                         0.364681000                   0.223413350
## 20                         0.046267400                  -0.218741396
## 21                        -0.085988050                  -0.176679685
## 22                        -0.075301650                  -0.302359265
## 23                         0.051482200                  -0.293115775
## 24                        -0.122194500                  -0.433696500
## 25                        -0.116438500                  -0.476461450
## 26                        -0.056087500                  -0.017115775
## 27                        -0.131634500                  -0.464962908
## 28                         0.285212000                   0.192277475
## 29                        -0.036385100                  -0.088007965
## 30                         0.159048000                   0.060734563
## 31                        -0.083197850                  -0.451720075
## 32                         0.339920500                   0.065538800
## 33                         0.025372200                  -0.237076322
## 34                         0.074231600                  -0.044846410
## 35                         0.121808000                   0.039002110
## 36                         0.167257500                   0.039002055
## 37                        -0.089648150                  -0.118422157
## 38                         0.020708000                  -0.177822963
## 39                        -0.097585050                  -0.142100685
## 40                        -0.133251500                  -0.173625852
## 41                         0.178609000                  -0.031212800
## 42                         0.038724500                  -0.103205915
## 43                         0.046958800                  -0.005554871
## 44                         0.011582900                   0.027303862
## 45                         0.419219000                   0.505240405
## 46                         0.280913000                   0.140894920
## 47                         0.160018500                   0.043417810
## 48                         0.050938250                   0.013991136
## 49                        -0.064607300                  -0.186366670
## 50                         0.173942500                   0.079413573
## 51                         0.044584900                  -0.007710054
## 52                        -0.023868100                  -0.223485280
## 53                         0.123214500                  -0.066184523
## 54                        -0.005374930                  -0.340256871
## 55                         0.049923150                  -0.028128980
## 56                         0.631915000                   0.464123675
## 57                         0.253026000                   0.134201625
## 58                         0.168506000                  -0.093252550
## 59                        -0.061383550                  -0.516235147
## 60                        -0.111813500                  -0.172946330
## 61                        -0.076446500                  -0.285886670
## 62                        -0.055217800                  -0.291368382
## 63                         0.158258000                   0.027513140
## 64                         0.047984450                  -0.284983443
## 65                         0.144099500                  -0.108369200
## 66                         0.565506000                   0.362265425
## 67                         0.262778500                   0.110703525
## 68                         0.051008600                  -0.004641115
## 69                         0.073376000                  -0.278184238
## 70                         0.253751000                   0.084087375
## 71                         0.094966200                  -0.070366978
## 72                         0.133759500                   0.046002878
## 73                         0.032373300                  -0.306348220
## 74                         0.203749000                   0.239213587
## 75                        -0.076747050                  -0.213408915
## 76                         0.044668950                  -0.103692455
## 77                         0.182130500                   0.068070177
## 78                        -0.081272150                  -0.113848432
## 79                         0.275050000                   0.089359775
## 80                         0.044526700                  -0.272589797
## 81                         0.027902650                  -0.128116218
## 82                        -0.018633000                  -0.470701645
## 83                         0.074763350                  -0.194667518
## 84                        -0.197973000                  -0.416983400
## 85                         0.051332300                  -0.025191365
## 86                         0.210266500                  -0.017393775
## 87                         0.163792000                   0.102724735
## 88                         0.047104400                  -0.086605135
## 89                         0.146509000                  -0.077046525
## 90                         0.058472650                  -0.099103558
## 91                        -0.089152000                  -0.198824725
## 92                        -0.043161700                  -0.094917775
## 93                         0.616771500                   0.471018875
## 94                        -0.134586500                  -0.155899129
## 95                         0.587364500                   0.357285550
## 96                         0.314615500                   0.248334008
## 97                        -0.122194500                  -0.433696500
## 98                         0.011582900                   0.027303862
## 99                         0.159681500                  -0.100487475
## 100                       -0.058433000                  -0.314704000
## 101                        0.378247000                   0.254932802
## 102                        0.141809500                  -0.078850147
## 103                        0.239286000                  -0.054904500
## 104                        0.251224000                   0.134362275
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## 554                       -0.068762850                  -0.088147220
## 555                        0.330933500                   0.226458400
## 556                        0.632823000                   0.476342550
## 557                        0.172889500                   0.067390450
## 558                        0.286482000                   0.116124740
## 559                        0.170898000                  -0.094735525
## 560                        0.046384250                  -0.124947523
## 561                        0.433146500                   0.493112690
## 562                        0.564611000                   0.794108075
## 563                        0.043282900                  -0.035498478
## 564                        0.168506000                  -0.093252550
## 565                        0.110309000                  -0.078685735
## 566                        0.182662000                   0.296427377
## 567                        0.328642000                   0.254242200
## 568                       -0.081831650                  -0.083666478
## 569                        0.204056000                  -0.008971825
## 570                        0.194244500                   0.249097501
## 571                        0.193385000                   0.247312195
## 572                        0.300381000                   0.297129795
## 573                        0.579429500                   0.799272000
## 574                        0.018193250                  -0.299333102
## 575                        0.202729500                   0.243361712
## 576                        0.334763000                   0.219981838
## 577                        0.170898000                  -0.094735525
## 578                        0.056667500                  -0.151978627
## 579                        0.333840500                   0.203171000
## 580                        0.023479950                  -0.277093715
## 581                        0.244149500                  -0.019698425
## 582                        0.413847000                   0.507775243
## 583                        0.200522500                  -0.003730263
## 584                       -0.072485600                  -0.007954608
## 585                        0.048013850                  -0.211027485
## 586                        0.400952500                   0.329919417
## 587                        0.326687500                   0.279148470
## 588                        0.277457500                   0.227581755
## 589                        0.243508000                   0.128899657
## 590                        0.300381000                   0.297129795
## 591                        0.148614000                  -0.254601350
## 592                        0.152201000                  -0.075535200
## 593                        0.419219000                   0.505240405
## 594                       -0.050412000                  -0.160758208
## 595                        0.041502750                   0.077589962
## 596                        0.130518500                   0.027104125
## 597                        0.356350000                   0.195476700
## 598                        0.332742000                   0.290501895
## 599                        0.327727500                   0.283515467
## 600                       -0.185932500                  -0.045329975
## 601                        0.576168500                   0.378225100
## 602                        0.254901500                   0.134376620
## 603                        0.051332300                  -0.025191365
## 604                        0.333870000                   0.259950375
## 605                        0.011582900                   0.027303862
## 606                        0.584157000                   0.382199675
## 607                        0.586174500                   0.382105775
## 608                        0.231141500                   0.001241475
## 609                        0.205544500                   0.121771692
## 610                        0.420203000                   0.512771575
## 611                        0.184152500                  -0.046156200
## 612                        0.413847000                   0.507775243
## 613                        0.063507600                   0.075110415
## 614                        0.282732500                   0.222248000
## 615                        0.286009500                   0.249629106
## 616                        0.247873500                  -0.033221050
## 617                        0.380782000                   0.286804958
## 618                        0.209702500                   0.146875275
## 619                        0.304557500                   0.252648476
## 620                        0.212899000                   0.135524625
## 621                        0.045259300                  -0.225269575
## 622                        0.637075500                   0.487633273
## 623                        0.168506000                  -0.093252550
## 624                        0.192555000                   0.233545845
## 625                        0.339165500                   0.218956850
## 626                        0.139869500                   0.067284214
## 627                        0.400952500                   0.329919417
## 628                        0.135562500                   0.013028820
## 629                        0.235174500                   0.049069875
## 630                        0.419219000                   0.505240405
## 631                        0.169290000                  -0.083355950
## 632                        0.188500000                   0.011770300
## 633                        0.579429500                   0.799272000
## 634                        0.579429500                   0.799272000
## 635                        0.579429500                   0.799272000
## 636                        0.638584500                   0.503133100
## 637                        0.378247000                   0.254932802
## 638                        0.239286000                  -0.054904500
## 639                        0.039067150                   0.006619512
## 640                        0.378972000                   0.284722520
## 641                        0.316107000                   0.244226058
## 642                        0.165116500                  -0.011249050
## 643                        0.131347500                   0.258204665
## 644                        0.404802500                   0.496833407
## 645                        0.260351000                   0.124012525
## 646                        0.002325855                  -0.319058410
## 647                        0.332850500                   0.216640202
## 648                        0.641571000                   0.487851550
## 649                       -0.056786750                   0.013807012
## 650                        0.170837500                   0.048132307
## 651                        0.186985500                   0.289804250
## 652                        0.037904750                  -0.003255563
## 653                        0.579429500                   0.799272000
## 654                        0.193595000                   0.081821130
## 655                        0.576168500                   0.378225100
## 656                        0.293539000                   0.245422417
## 657                        0.066865900                  -0.184112740
## 658                        0.100796500                   0.055031494
## 659                        0.193385000                   0.247312195
## 660                        0.586387000                   0.380563275
## 661                        0.208433500                   0.131590110
## 662                        0.173222000                   0.226483325
## 663                        0.173622000                   0.053635600
## 664                        0.637075500                   0.487633273
## 665                        0.419219000                   0.505240405
## 666                        0.324001500                   0.288896998
## 667                        0.168715500                   0.060021975
## 668                        0.215662500                  -0.017901000
## 669                        0.372212500                   0.329753795
## 670                        0.390754500                   0.313323115
## 671                        0.090340950                   0.070110560
## 672                        0.221142500                   0.025240175
## 673                       -0.247517000                  -0.527050300
## 674                        0.135867500                   0.141837910
## 675                        0.420442500                   0.503605475
## 676                        0.246287000                   0.136201925
## 677                        0.193604000                   0.241997140
## 678                        0.587364500                   0.357285550
## 679                        0.339869000                   0.220433113
## 680                        0.284409000                   0.136419300
## 681                        0.404430000                   0.480990300
## 682                        0.332813000                   0.297905708
## 683                        0.294050000                   0.139238800
## 684                        0.320912000                   0.286819288
## 685                        0.166947500                   0.061791655
## 686                        0.568681000                   0.801556400
## 687                        0.378247000                   0.254932802
## 688                        0.154537500                   0.063093913
## 689                        0.264816000                   0.220715058
## 690                       -0.193702500                  -0.049919000
## 691                        0.307454000                   0.246832562
## 692                        0.129894500                   0.167259350
## 693                        0.339869000                   0.220433113
## 694                        0.396153500                   0.458648128
## 695                        0.397086500                   0.476766125
## 696                        0.404802500                   0.496833407
## 697                        0.181122500                   0.016102700
## 698                        0.193385000                   0.247312195
## 699                        0.413847000                   0.507775243
## 700                        0.641571000                   0.487851550
## 701                        0.413847000                   0.507775243
## 702                        0.284409000                   0.136419300
## 703                        0.431583000                   0.506201215
## 704                        0.312171500                   0.284407205
## 705                        0.149668500                   0.062578860
## 706                        0.150355000                   0.098703841
## 707                        0.003603880                  -0.148531483
## 708                        0.400952500                   0.329919417
## 709                        0.627790000                   0.490132498
## 710                        0.213098000                   0.133234450
## 711                        0.265778000                   0.212249688
## 712                        0.638584500                   0.503133100
## 713                        0.159681500                  -0.100487475
## 714                        0.066783450                   0.015132693
## 715                        0.332742000                   0.290501895
## 716                        0.576168500                   0.378225100
## 717                        0.584157000                   0.382199675
## 718                        0.377824500                   0.335484608
## 719                        0.288422500                   0.163150857
## 720                        0.212899000                   0.135524625
## 721                        0.334763000                   0.219981838
## 722                        0.306848000                   0.232029355
## 723                        0.433146500                   0.493112690
## 724                        0.380782000                   0.286804958
## 725                        0.251316000                   0.065769275
## 726                        0.165116500                  -0.011249050
## 727                        0.329804500                   0.228164673
## 728                        0.637075500                   0.487633273
## 729                        0.320912000                   0.286819288
## 730                        0.564589500                   0.794460925
## 731                        0.635625500                   0.463812728
## 732                        0.580976500                   0.808348450
## 733                        0.562494000                   0.824351450
## 734                       -0.005388805                   0.053629794
## 735                        0.629848000                   0.466801150
## 736                        0.165116500                  -0.011249050
## 737                        0.194244500                   0.249097501
## 738                        0.332813000                   0.297905708
## 739                        0.280064000                   0.251354296
## 740                        0.586646000                   0.387071650
## 741                        0.202729500                   0.243361712
## 742                        0.285574000                   0.222850992
## 743                        0.209888500                   0.141826992
## 744                        0.420203000                   0.512771575
## 745                        0.404802500                   0.496833407
## 746                        0.651994500                   0.565758170
## 747                        0.636561500                   0.491928825
## 748                        0.582057000                   0.381105500
## 749                        0.633016500                   0.492171750
## 750                        0.275056000                   0.086125825
## 751                        0.193385000                   0.247312195
## 752                        0.563468500                   0.795003200
## 753                        0.685627000                   0.576100648
## 754                        0.333940000                   0.293273045
## 755                        0.268719500                   0.215553602
## 756                        0.641571000                   0.487851550
## 757                        0.561482000                   0.826457875
## 758                        0.678800000                   0.574181625
## 759                        0.431583000                   0.506201215
## 760                        0.579429500                   0.799272000
## 761                        0.568033000                   0.827597475
## 762                        0.062023950                   0.064873600
## 763                        0.584157000                   0.382199675
## 764                        0.339869000                   0.220433113
## 765                        0.413712000                   0.509396690
## 766                        0.273776500                   0.080265725
## 767                        0.633889500                   0.498926225
## 768                        0.633889500                   0.498926225
## 769                        0.285574000                   0.222850992
## 770                        0.333461000                   0.214925420
## 771                        0.339165500                   0.218956850
## 772                        0.372212500                   0.329753795
## 773                        0.039067150                   0.006619512
## 774                        0.225972500                   0.078745050
## 775                        0.672798000                   0.571886015
## 776                        0.666847000                   0.564883494
## 777                        0.633889500                   0.498926225
## 778                        0.653238500                   0.554501225
## 779                        0.408339000                   0.503615625
## 780                        0.641571000                   0.487851550
## 781                        0.324001500                   0.288896998
## 782                        0.304268000                   0.124070500
## 783                        0.564589500                   0.794460925
## 784                        0.577719000                   0.363898450
## 785                        0.633889500                   0.498926225
## 786                        0.584157000                   0.382199675
## 787                        0.562255000                   0.793505675
## 788                        0.555125500                   0.760241100
## 789                        0.568033000                   0.827597475
## 790                        0.370343500                   0.212066750
## 791                        0.633889500                   0.498926225
## 792                        0.376373500                   0.334968058
## 793                        0.580976500                   0.808348450
## 794                        0.686911500                   0.564208700
## 795                        0.562255000                   0.793505675
## 796                        0.298437000                   0.279857173
## 797                        0.564589500                   0.794460925
## 798                        0.562255000                   0.793505675
## 799                        0.579429500                   0.799272000
## 800                        0.583397500                   0.364773325
## 801                        0.651708000                   0.570939720
## 802                        0.641571000                   0.487851550
## 803                        0.563937000                   0.801524925
## 804                        0.568681000                   0.801556400
## 805                        0.373025500                   0.327637873
## 806                        0.584157000                   0.382199675
## 807                        0.564122500                   0.825623925
## 808                        0.582451500                   0.360798250
## 809                        0.562494000                   0.824351450
## 810                        0.631915000                   0.464123675
## 811                        0.564122500                   0.825623925
## 812                        0.562255000                   0.793505675
## 813                        0.586387000                   0.380563275
##     lower.025_q_grass_skill_winner lower.025_q_hard_skill_winner
## 1                    -0.0721432525                 -0.0257676625
## 2                    -0.2601683075                 -0.2453951500
## 3                     0.1392247125                  0.1400741000
## 4                     0.0727872025                  0.0872196750
## 5                    -0.0987661625                 -0.0725500650
## 6                    -0.0542712490                 -0.0904454000
## 7                     0.0958577250                  0.2039220750
## 8                    -0.0945230375                 -0.0408211775
## 9                     0.0368174775                  0.0797491075
## 10                    0.0878127000                  0.1476532250
## 11                    0.1505909500                  0.3356262000
## 12                    0.2460398775                  0.3606024500
## 13                   -0.2379086300                 -0.2051790250
## 14                    0.1324649000                  0.3072381750
## 15                   -0.2161327300                 -0.1933061000
## 16                    0.0777859250                  0.1822754500
## 17                    0.0790424750                  0.2568197250
## 18                   -0.1888238750                 -0.1368026500
## 19                    0.2561552875                  0.3021988500
## 20                   -0.0479737400                 -0.0426267400
## 21                   -0.3917232900                 -0.3408836750
## 22                   -0.2732388675                 -0.2284782750
## 23                   -0.1139159360                 -0.0620035925
## 24                   -0.2001812320                 -0.2264969250
## 25                   -0.1636823612                 -0.2290853250
## 26                   -0.1937507150                 -0.1650611500
## 27                   -0.2156927175                 -0.2713048500
## 28                    0.0958577250                  0.2039220750
## 29                   -0.1561866300                 -0.1397295250
## 30                    0.0143259525                  0.0931138375
## 31                   -0.1974226275                 -0.1730332750
## 32                    0.2518452225                  0.2690548750
## 33                   -0.0965985509                 -0.0681999725
## 34                   -0.0126086250                 -0.0119515500
## 35                    0.0464417275                  0.0532087700
## 36                    0.0571654125                  0.0724957800
## 37                   -0.2115336925                 -0.2040263250
## 38                   -0.1346905000                 -0.0824423100
## 39                   -0.3312603500                 -0.2381038250
## 40                   -0.2742681050                 -0.2384874250
## 41                    0.0014699250                  0.1005121800
## 42                   -0.1052607750                 -0.0722987100
## 43                   -0.1026361975                 -0.0442077625
## 44                   -0.2162200575                 -0.1433825250
## 45                    0.2438277525                  0.3558065500
## 46                    0.1059338500                  0.2225294250
## 47                    0.0102757175                  0.0891627825
## 48                   -0.1142081725                 -0.0450614650
## 49                   -0.2490296275                 -0.2234410500
## 50                    0.0409407325                  0.0978605200
## 51                   -0.0921024283                 -0.0609909575
## 52                   -0.2050670625                 -0.1743942250
## 53                    0.0377475253                  0.0255676250
## 54                    0.0029150300                 -0.0796487875
## 55                   -0.0779997747                 -0.0446676075
## 56                    0.4301559500                  0.5654434000
## 57                    0.0669251000                  0.1859172750
## 58                    0.0885355350                  0.0952462725
## 59                   -0.1948448725                 -0.1618883500
## 60                   -0.3473654750                 -0.2801093250
## 61                   -0.2664928500                 -0.1986659500
## 62                   -0.2757853925                 -0.2022274000
## 63                    0.0217146450                  0.0840506050
## 64                   -0.1353657575                 -0.1499822750
## 65                    0.0097065800                  0.0665865225
## 66                    0.4838065650                  0.5110756000
## 67                    0.1586431850                  0.2022886750
## 68                   -0.0546248450                 -0.0345636500
## 69                   -0.1871345050                 -0.1525074500
## 70                    0.0498307750                  0.1829162500
## 71                   -0.0055883830                  0.0010548435
## 72                    0.0483084475                  0.0658309075
## 73                   -0.1191068780                 -0.0899894575
## 74                    0.0076804250                  0.1203120500
## 75                   -0.2431735325                 -0.2070240500
## 76                   -0.0778718200                 -0.0529102225
## 77                    0.0129459000                  0.1109850250
## 78                   -0.2069299675                 -0.2001004750
## 79                    0.1227788525                  0.2074105500
## 80                   -0.1071086150                 -0.0764426200
## 81                   -0.1567908938                 -0.0992487825
## 82                   -0.1067484775                 -0.1161618750
## 83                   -0.0632760283                 -0.0194770000
## 84                   -0.3190291225                 -0.3241146000
## 85                   -0.2422201975                 -0.2022936000
## 86                    0.0701176225                  0.0878260275
## 87                   -0.0028077250                  0.0897438075
## 88                   -0.0385607525                 -0.0411403100
## 89                    0.0285786000                  0.0766086125
## 90                   -0.0430366735                 -0.0395723800
## 91                   -0.4035942500                 -0.3345383000
## 92                   -0.1837975208                 -0.1766940250
## 93                    0.4803738750                  0.5606175750
## 94                   -0.2568930387                 -0.2348893500
## 95                    0.4880433875                  0.5234726750
## 96                    0.1301519500                  0.2468049750
## 97                   -0.2001812320                 -0.2264969250
## 98                   -0.2162200575                 -0.1433825250
## 99                    0.0862149550                  0.0871349100
## 100                  -0.2843537175                 -0.2683171000
## 101                   0.2707422000                  0.3189088000
## 102                   0.0179406475                  0.0632649050
## 103                   0.1028631450                  0.1777202000
## 104                   0.0653574250                  0.1880194500
## 105                  -0.0280034125                 -0.0181280600
## 106                  -0.1961655300                 -0.1562779000
## 107                   0.4355915500                  0.5670171500
## 108                  -0.1316543725                 -0.0631103400
## 109                  -0.5003928500                 -0.3454779500
## 110                  -0.3731026425                 -0.3694665250
## 111                   0.0640093750                  0.1767679000
## 112                  -0.2439520042                 -0.2114912250
## 113                  -0.0704786035                 -0.0145865900
## 114                  -0.0779997747                 -0.0446676075
## 115                  -0.1668536675                 -0.0830766600
## 116                  -0.1927885700                 -0.1142540250
## 117                  -0.1345992645                 -0.1198683500
## 118                   0.0179406475                  0.0632649050
## 119                   0.4596109750                  0.5709655250
## 120                   0.0029150300                 -0.0796487875
## 121                   0.0097065800                  0.0665865225
## 122                  -0.0425472500                 -0.0194862175
## 123                   0.0831334425                  0.0586137275
## 124                   0.1586431850                  0.2022886750
## 125                  -0.1443329500                 -0.0784414025
## 126                  -0.2103228425                 -0.1982695250
## 127                   0.0773101775                  0.1571741750
## 128                   0.0253040450                  0.0525774075
## 129                  -0.1009844725                 -0.0415051325
## 130                  -0.0977669318                 -0.0478298475
## 131                   0.0313072100                  0.0778863225
## 132                  -0.0612275287                 -0.0252688450
## 133                  -0.2546402725                 -0.2075027250
## 134                   0.2720929650                  0.3229033250
## 135                  -0.1142081725                 -0.0450614650
## 136                   0.0191829225                  0.1232110500
## 137                  -0.0113138626                  0.0010807169
## 138                   0.0482203000                  0.2606093250
## 139                  -0.0260114000                  0.0509781825
## 140                  -0.0426183550                  0.0418059775
## 141                  -0.0069861075                  0.1030816250
## 142                  -0.2141444825                 -0.1670056250
## 143                  -0.0616410225                 -0.0294335300
## 144                   0.0390796825                  0.0858368050
## 145                   0.0655040980                  0.0341512000
## 146                   0.0099568250                  0.0928994475
## 147                   0.0701816750                  0.1806589000
## 148                  -0.1803438625                 -0.1372965750
## 149                  -0.2051144975                 -0.1096129750
## 150                  -0.0014795000                  0.0984388875
## 151                  -0.2009231470                 -0.1966737000
## 152                  -0.1072652300                  0.0325368925
## 153                  -0.0055883830                  0.0010548435
## 154                  -0.1674740451                 -0.1031187750
## 155                  -0.1590788350                 -0.1644400750
## 156                  -0.0779997747                 -0.0446676075
## 157                   0.0497991375                  0.1154728750
## 158                  -0.1920463300                 -0.0982572200
## 159                  -0.0891046375                 -0.0565079025
## 160                  -0.2440406475                 -0.2281029250
## 161                  -0.2020513168                 -0.1621348000
## 162                  -0.1818751654                 -0.1070601500
## 163                  -0.0019666050                 -0.0649298400
## 164                  -0.4964916250                 -0.4600939250
## 165                  -0.0387539350                  0.0049644752
## 166                  -0.4321289000                 -0.2960439750
## 167                   0.2707422000                  0.3189088000
## 168                  -0.2739357800                 -0.2361127750
## 169                   0.4606870750                  0.5757182500
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## 594                  -0.2205676800                 -0.2070587250
## 595                  -0.1045185815                 -0.0411373675
## 596                   0.0866568745                  0.0649079200
## 597                   0.2497836150                  0.2915393250
## 598                   0.0650502750                  0.2620319000
## 599                   0.0818237250                  0.2615536750
## 600                  -0.4361143750                 -0.2945147250
## 601                   0.4202985500                  0.5087338500
## 602                   0.0702571250                  0.1851123000
## 603                  -0.2422201975                 -0.2022936000
## 604                   0.0609560750                  0.2625477000
## 605                  -0.2162200575                 -0.1433825250
## 606                   0.4531624250                  0.5178450250
## 607                   0.4596300500                  0.5217087750
## 608                   0.1490806800                  0.1621288000
## 609                   0.1164451800                  0.1400514750
## 610                   0.2556752500                  0.3638403250
## 611                   0.0775907150                  0.1063505250
## 612                   0.2387427500                  0.3491500500
## 613                  -0.0367269292                 -0.0120427300
## 614                   0.1448820025                  0.2097820250
## 615                   0.0985735500                  0.2167751000
## 616                   0.0903089250                  0.1807437750
## 617                   0.2711024675                  0.3239717000
## 618                   0.1248798025                  0.1468220000
## 619                   0.1369371500                  0.2439471500
## 620                   0.0690130250                  0.1405927500
## 621                  -0.0740236700                 -0.0430922075
## 622                   0.4695457500                  0.5706584250
## 623                   0.0885355350                  0.0952462725
## 624                  -0.0085685750                  0.1117176750
## 625                   0.2109132250                  0.2758178000
## 626                   0.0154397600                  0.0552631200
## 627                   0.2729581050                  0.3442923250
## 628                  -0.0260114000                  0.0509781825
## 629                   0.1801413557                  0.1426585750
## 630                   0.2438277525                  0.3558065500
## 631                   0.0898603625                  0.0941927400
## 632                   0.0251884550                  0.1200590250
## 633                   0.3421729750                  0.5167614500
## 634                   0.3421729750                  0.5167614500
## 635                   0.3421729750                  0.5167614500
## 636                   0.4650024250                  0.5760639750
## 637                   0.2707422000                  0.3189088000
## 638                   0.1028631450                  0.1777202000
## 639                  -0.1020001700                 -0.0490172125
## 640                   0.2606419350                  0.3221170250
## 641                   0.1826034575                  0.2567951500
## 642                   0.0609896163                  0.0710366500
## 643                  -0.0770599150                  0.0518940950
## 644                   0.1531600000                  0.3335340500
## 645                   0.0504770750                  0.1870265250
## 646                  -0.1837065925                 -0.1617492500
## 647                   0.1599720750                  0.2695912250
## 648                   0.4642691500                  0.5765676000
## 649                  -0.2233579275                 -0.1800144250
## 650                   0.0169191750                  0.0950568800
## 651                   0.0266542550                  0.1181100000
## 652                  -0.0983214800                 -0.0465219675
## 653                   0.3421729750                  0.5167614500
## 654                   0.0478054250                  0.1288060250
## 655                   0.4202985500                  0.5087338500
## 656                   0.1095932600                  0.2214062750
## 657                   0.0352580600                 -0.0098434697
## 658                  -0.1419978975                  0.0163579825
## 659                   0.0112054500                  0.1084672250
## 660                   0.4606470000                  0.5204411750
## 661                   0.1191549700                  0.1384784500
## 662                  -0.0632889175                  0.0795366375
## 663                   0.0575497125                  0.0717540500
## 664                   0.4695457500                  0.5706584250
## 665                   0.2438277525                  0.3558065500
## 666                   0.0793844250                  0.2565314750
## 667                   0.0004037250                  0.1028325250
## 668                   0.1195543300                  0.1368981000
## 669                   0.2399978275                  0.3091468000
## 670                   0.2665046200                  0.3304679250
## 671                   0.0079628400                  0.0231116800
## 672                   0.0683143500                  0.1467746000
## 673                  -0.4621849900                 -0.4785732250
## 674                  -0.1026131500                  0.0419347525
## 675                   0.2421817250                  0.3591427500
## 676                   0.0777859250                  0.1822754500
## 677                   0.0011759000                  0.1173880250
## 678                   0.4880433875                  0.5234726750
## 679                   0.2173538300                  0.2810883000
## 680                   0.1016963250                  0.2184835000
## 681                   0.1505909500                  0.3356262000
## 682                   0.0626016500                  0.2598082250
## 683                   0.1069481500                  0.2274409500
## 684                   0.0823551000                  0.2545082750
## 685                  -0.0004687000                  0.1043955000
## 686                   0.3385114750                  0.5089095750
## 687                   0.2707422000                  0.3189088000
## 688                   0.0049198500                  0.0895421600
## 689                   0.1293647350                  0.1929199250
## 690                  -0.4321289000                 -0.2960439750
## 691                   0.1639546500                  0.2459023750
## 692                  -0.0713839775                  0.0441852375
## 693                   0.2173538300                  0.2810883000
## 694                   0.1457195250                  0.3262597000
## 695                   0.1465383500                  0.3279147750
## 696                   0.1531600000                  0.3335340500
## 697                   0.0090054575                  0.1011068000
## 698                   0.0112054500                  0.1084672250
## 699                   0.2387427500                  0.3491500500
## 700                   0.4642691500                  0.5765676000
## 701                   0.2387427500                  0.3491500500
## 702                   0.1016963250                  0.2184835000
## 703                   0.2499292250                  0.3702529000
## 704                   0.0835874000                  0.2467951500
## 705                  -0.0395838750                  0.0793311975
## 706                  -0.0284132250                  0.0768683450
## 707                  -0.1456394075                 -0.1244688000
## 708                   0.2729581050                  0.3442923250
## 709                   0.4650885750                  0.5678712000
## 710                   0.0717321825                  0.1402094250
## 711                   0.1159687500                  0.1939151500
## 712                   0.4650024250                  0.5760639750
## 713                   0.0862149550                  0.0871349100
## 714                  -0.2498448275                 -0.1716907500
## 715                   0.0650502750                  0.2620319000
## 716                   0.4202985500                  0.5087338500
## 717                   0.4531624250                  0.5178450250
## 718                   0.2489700175                  0.3137639500
## 719                   0.1312817500                  0.2275802000
## 720                   0.0690130250                  0.1405927500
## 721                   0.1661501250                  0.2690580500
## 722                   0.1638966250                  0.2398931750
## 723                   0.2545176500                  0.3714312750
## 724                   0.2711024675                  0.3239717000
## 725                   0.0615495500                  0.1787624750
## 726                   0.0609896163                  0.0710366500
## 727                   0.0758692250                  0.2556313750
## 728                   0.4695457500                  0.5706584250
## 729                   0.0823551000                  0.2545082750
## 730                   0.3392659500                  0.4970091750
## 731                   0.4288225500                  0.5714310250
## 732                   0.3435099250                  0.5216689500
## 733                   0.3362782750                  0.4947069500
## 734                  -0.1782717425                 -0.1238028500
## 735                   0.4740422525                  0.5728211000
## 736                   0.0609896163                  0.0710366500
## 737                  -0.0497451250                  0.1060111250
## 738                   0.0626016500                  0.2598082250
## 739                   0.1032227750                  0.2040417750
## 740                   0.4580881325                  0.5202018000
## 741                   0.0041926750                  0.1175159000
## 742                   0.1490563250                  0.2189511500
## 743                   0.1246218150                  0.1402678500
## 744                   0.2556752500                  0.3638403250
## 745                   0.1531600000                  0.3335340500
## 746                   0.4414438250                  0.5874804500
## 747                   0.4594618250                  0.5745295000
## 748                   0.4542584575                  0.5148249250
## 749                   0.4630421000                  0.5726967000
## 750                   0.0976523875                  0.2005637250
## 751                   0.0112054500                  0.1084672250
## 752                   0.3356480750                  0.4991717250
## 753                   0.4837458000                  0.6287311750
## 754                   0.0482203000                  0.2606093250
## 755                   0.1054036250                  0.1912358750
## 756                   0.4642691500                  0.5765676000
## 757                   0.3291487500                  0.4953888250
## 758                   0.4590804500                  0.6169385750
## 759                   0.2499292250                  0.3702529000
## 760                   0.3421729750                  0.5167614500
## 761                   0.3179972000                  0.5007633250
## 762                  -0.0607612957                 -0.0247013800
## 763                   0.4531624250                  0.5178450250
## 764                   0.2173538300                  0.2810883000
## 765                   0.2479320250                  0.3559219500
## 766                   0.0983846525                  0.2030360250
## 767                   0.4596109750                  0.5709655250
## 768                   0.4596109750                  0.5709655250
## 769                   0.1490563250                  0.2189511500
## 770                   0.1687545500                  0.2710252000
## 771                   0.2109132250                  0.2758178000
## 772                   0.2399978275                  0.3091468000
## 773                  -0.1020001700                 -0.0490172125
## 774                   0.0879547250                  0.1655669000
## 775                   0.4585638000                  0.6098572500
## 776                   0.4553592250                  0.6015087000
## 777                   0.4596109750                  0.5709655250
## 778                   0.4032625000                  0.5886340500
## 779                   0.2243403750                  0.3385108500
## 780                   0.4642691500                  0.5765676000
## 781                   0.0793844250                  0.2565314750
## 782                   0.1426413750                  0.2298618500
## 783                   0.3392659500                  0.4970091750
## 784                   0.4243695250                  0.5104124750
## 785                   0.4596109750                  0.5709655250
## 786                   0.4531624250                  0.5178450250
## 787                   0.3281262250                  0.4972278500
## 788                   0.3066756750                  0.4894275000
## 789                   0.3179972000                  0.5007633250
## 790                   0.2593866225                  0.3068080250
## 791                   0.4596109750                  0.5709655250
## 792                   0.2468188500                  0.3140277750
## 793                   0.3435099250                  0.5216689500
## 794                   0.4686885750                  0.6257347250
## 795                   0.3281262250                  0.4972278500
## 796                   0.1265676850                  0.2292674750
## 797                   0.3392659500                  0.4970091750
## 798                   0.3281262250                  0.4972278500
## 799                   0.3421729750                  0.5167614500
## 800                   0.4135361250                  0.5126634500
## 801                   0.4050492750                  0.5836854500
## 802                   0.4642691500                  0.5765676000
## 803                   0.3447489750                  0.4972012000
## 804                   0.3385114750                  0.5089095750
## 805                   0.2400892750                  0.3107985750
## 806                   0.4531624250                  0.5178450250
## 807                   0.3406312000                  0.4980394750
## 808                   0.4225664000                  0.5100285500
## 809                   0.3362782750                  0.4947069500
## 810                   0.4301559500                  0.5654434000
## 811                   0.3406312000                  0.4980394750
## 812                   0.3281262250                  0.4972278500
## 813                   0.4606470000                  0.5204411750
##     upper.975_q_clay_skill_winner upper.975_q_grass_skill_winner
## 1                     0.022327577                    0.243014045
## 2                     0.096417665                    0.140315950
## 3                     0.221797422                    0.329749782
## 4                     0.187393900                    0.354371450
## 5                     0.256268382                    0.162561090
## 6                    -0.077466163                    0.181668259
## 7                     0.404682447                    0.364360325
## 8                     0.202815133                    0.172470725
## 9                     0.179409465                    0.247366040
## 10                    0.271408357                    0.326727500
## 11                    0.653152600                    0.409248330
## 12                    0.650966450                    0.439229192
## 13                    0.175671397                    0.082153250
## 14                    0.636646625                    0.399132533
## 15                    0.091544190                    0.099400542
## 16                    0.314537750                    0.293841275
## 17                    0.450222000                    0.322837107
## 18                    0.251724037                    0.126933388
## 19                    0.427099520                    0.462227990
## 20                    0.114071735                    0.198966492
## 21                    0.239985425                    0.175460715
## 22                    0.246502262                    0.065360956
## 23                    0.241825052                    0.234425015
## 24                   -0.024394488                    0.078115610
## 25                    0.060253075                    0.106923695
## 26                    0.244525094                    0.117167612
## 27                    0.095743805                    0.130671546
## 28                    0.404682447                    0.364360325
## 29                    0.183380145                    0.092906542
## 30                    0.225518127                    0.219327152
## 31                   -0.040098013                    0.082295780
## 32                    0.296566372                    0.471759200
## 33                    0.068241770                    0.156482132
## 34                    0.125559910                    0.228142012
## 35                    0.252639065                    0.254654322
## 36                    0.351484025                    0.340842025
## 37                    0.118474635                    0.086107957
## 38                    0.091492265                    0.160603082
## 39                    0.176126375                    0.098708145
## 40                    0.106429507                    0.048613302
## 41                    0.296987937                    0.293596060
## 42                    0.181173465                    0.193391690
## 43                    0.205578962                    0.158129585
## 44                    0.269815840                    0.187644350
## 45                    0.669309950                    0.465873320
## 46                    0.351703755                    0.346623582
## 47                    0.249124660                    0.271220025
## 48                    0.236588645                    0.167216557
## 49                    0.242425750                    0.107737760
## 50                    0.270605477                    0.293320712
## 51                    0.262284240                    0.178202540
## 52                    0.133042442                    0.168393347
## 53                    0.306933300                    0.246275552
## 54                    0.011835717                    0.238781442
## 55                    0.181624580                    0.172541167
## 56                    0.675930345                    0.666100282
## 57                    0.318032185                    0.291062997
## 58                    0.174272810                    0.345525875
## 59                   -0.071035090                    0.105667375
## 60                    0.122506485                    0.114924257
## 61                    0.240959150                    0.050541049
## 62                    0.264610212                    0.124950343
## 63                    0.228272170                    0.257120017
## 64                    0.225387382                    0.265928680
## 65                    0.149721902                    0.256969500
## 66                    0.555036638                    0.669810702
## 67                    0.279661057                    0.363346317
## 68                    0.209009022                    0.184846230
## 69                    0.287447020                    0.332671100
## 70                    0.320217478                    0.308668710
## 71                    0.111713846                    0.291022012
## 72                    0.256655150                    0.265690700
## 73                    0.214480007                    0.214026317
## 74                    0.400960375                    0.270145800
## 75                    0.183804725                    0.097251854
## 76                    0.133445680                    0.204579725
## 77                    0.266285932                    0.236356360
## 78                    0.120826922                    0.091390270
## 79                    0.283563335                    0.335547350
## 80                    0.063678032                    0.197022022
## 81                    0.215377820                    0.159361603
## 82                   -0.111844488                    0.155378382
## 83                    0.209963012                    0.186310047
## 84                   -0.029261438                    0.003360350
## 85                    0.292175982                    0.307340945
## 86                    0.296674322                    0.359137875
## 87                    0.314009550                    0.234673745
## 88                    0.116037635                    0.229539380
## 89                    0.151641150                    0.236886197
## 90                    0.119676160                    0.251632147
## 91                    0.248913600                    0.171070862
## 92                    0.192707368                    0.141123387
## 93                    0.642121240                    0.658946985
## 94                    0.101115825                    0.020271227
## 95                    0.564735920                    0.665414817
## 96                    0.407249425                    0.342730730
## 97                   -0.024394488                    0.078115610
## 98                    0.269815840                    0.187644350
## 99                    0.155131190                    0.330233575
## 100                   0.188794490                    0.135893765
## 101                   0.450025980                    0.462418385
## 102                   0.148952932                    0.231649747
## 103                   0.189969725                    0.324904598
## 104                   0.316962710                    0.300407408
## 105                   0.345623760                    0.207619992
## 106                   0.212624175                    0.135417487
## 107                   0.682285542                    0.675436932
## 108                   0.099083012                    0.169197385
## 109                   0.162688925                   -0.109486638
## 110                  -0.003665715                   -0.023751635
## 111                   0.300075427                    0.298470927
## 112                   0.181862487                    0.089167020
## 113                   0.218036982                    0.193101427
## 114                   0.181624580                    0.172541167
## 115                   0.177903187                    0.109659397
## 116                   0.237264635                    0.094030840
## 117                   0.111264978                    0.149487465
## 118                   0.148952932                    0.231649747
## 119                   0.685160160                    0.654742060
## 120                   0.011835717                    0.238781442
## 121                   0.149721902                    0.256969500
## 122                   0.015040194                    0.222966390
## 123                   0.219010785                    0.283748325
## 124                   0.279661057                    0.363346317
## 125                   0.368506940                    0.257901675
## 126                   0.126303855                    0.091110550
## 127                   0.279638145                    0.298643727
## 128                   0.293526675                    0.275313177
## 129                   0.237481337                    0.161609797
## 130                   0.202186932                    0.144545952
## 131                   0.222457327                    0.241333800
## 132                   0.131263562                    0.189509685
## 133                   0.167238122                    0.076051319
## 134                   0.472409507                    0.458700370
## 135                   0.236588645                    0.167216557
## 136                   0.287638625                    0.267240710
## 137                   0.118920070                    0.246873750
## 138                   0.487635225                    0.325790825
## 139                   0.253265112                    0.270769610
## 140                   0.171120922                    0.220193470
## 141                   0.395877615                    0.249659580
## 142                   0.215677717                    0.132489405
## 143                   0.199387844                    0.198975868
## 144                   0.233361140                    0.255282402
## 145                   0.083207562                    0.294298225
## 146                   0.232119975                    0.219698313
## 147                   0.270512902                    0.350868065
## 148                   0.184725130                    0.136398110
## 149                   0.232609341                    0.092826800
## 150                   0.266885765                    0.249544590
## 151                   0.048149637                    0.089131227
## 152                   0.327884500                    0.180082102
## 153                   0.111713846                    0.291022012
## 154                   0.242587101                    0.097157677
## 155                   0.217668487                    0.140602255
## 156                   0.181624580                    0.172541167
## 157                   0.311664025                    0.325641275
## 158                   0.239960360                    0.119845327
## 159                   0.273867915                    0.180300125
## 160                   0.121210175                    0.036661125
## 161                   0.110115072                    0.188408020
## 162                   0.098664969                    0.127660770
## 163                   0.126470782                    0.269928595
## 164                  -0.025759125                   -0.086044375
## 165                   0.221831020                    0.199336015
## 166                   0.130360800                   -0.112191745
## 167                   0.450025980                    0.462418385
## 168                   0.178919352                    0.111086230
## 169                   0.682731739                    0.654400277
## 170                   0.075597735                    0.041598187
## 171                   0.098436797                    0.231729537
## 172                   0.230448110                    0.324261645
## 173                   0.023186497                    0.233538050
## 174                   0.112938298                    0.255280063
## 175                   0.180957910                    0.109902432
## 176                   0.245693270                    0.335872285
## 177                   0.297422127                    0.266098775
## 178                   0.178919352                    0.111086230
## 179                   0.320217478                    0.308668710
## 180                   0.235528187                    0.086058750
## 181                   0.240488215                    0.242522917
## 182                   0.392229800                    0.261764519
## 183                   0.146722640                    0.115050160
## 184                   0.250888107                    0.071465120
## 185                  -0.012755435                    0.069887042
## 186                   0.268925625                    0.262117512
## 187                   0.215377820                    0.159361603
## 188                   0.194484202                    0.091986662
## 189                   0.013221395                    0.095265387
## 190                   0.022457503                    0.276617497
## 191                   0.189659625                    0.059136622
## 192                   0.203610070                    0.242264622
## 193                   0.027774710                    0.264572150
## 194                   0.143750702                    0.322467257
## 195                   0.350046897                    0.204714533
## 196                   0.148952932                    0.231649747
## 197                   0.106289917                   -0.009787705
## 198                   0.222878115                    0.321638962
## 199                  -0.030261400                   -0.032448848
## 200                   0.267713709                    0.067184847
## 201                   0.282672702                    0.188171602
## 202                   0.218036982                    0.193101427
## 203                   0.411942200                    0.388593451
## 204                   0.292945025                    0.230604472
## 205                  -0.055507665                    0.084255795
## 206                   0.239165677                    0.360183325
## 207                   0.666309175                    0.466299769
## 208                   0.487550200                    0.355306797
## 209                   0.464026800                    0.325073722
## 210                   0.256655150                    0.265690700
## 211                   0.669202250                    0.474651972
## 212                   0.244706152                    0.207580282
## 213                   0.289651912                    0.275982160
## 214                   0.346320460                    0.360979300
## 215                   0.101197770                    0.147060645
## 216                  -0.066554250                    0.193456823
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## 674                   0.342167612                    0.188407075
## 675                   0.666309175                    0.466299769
## 676                   0.314537750                    0.293841275
## 677                   0.397229800                    0.262873627
## 678                   0.564735920                    0.665414817
## 679                   0.391146017                    0.417173962
## 680                   0.359334705                    0.350000967
## 681                   0.653152600                    0.409248330
## 682                   0.474156050                    0.343521375
## 683                   0.362411827                    0.350451505
## 684                   0.455348797                    0.322902300
## 685                   0.258738575                    0.225566002
## 686                   0.980589475                    0.567818102
## 687                   0.450025980                    0.462418385
## 688                   0.230939837                    0.212403880
## 689                   0.421845450                    0.373317880
## 690                   0.130360800                   -0.112191745
## 691                   0.428047962                    0.411344310
## 692                   0.338282425                    0.199113816
## 693                   0.391146017                    0.417173962
## 694                   0.645069450                    0.414098704
## 695                   0.655558125                    0.402762259
## 696                   0.661174650                    0.414714292
## 697                   0.273769036                    0.275886332
## 698                   0.410188200                    0.259046597
## 699                   0.667449900                    0.462925920
## 700                   0.690767022                    0.656522107
## 701                   0.667449900                    0.462925920
## 702                   0.359334705                    0.350000967
## 703                   0.669202250                    0.474651972
## 704                   0.454933457                    0.311476130
## 705                   0.292945025                    0.230604472
## 706                   0.314188100                    0.222793532
## 707                   0.197119397                    0.196805097
## 708                   0.497705472                    0.475261697
## 709                   0.679496330                    0.658575215
## 710                   0.333405032                    0.314880012
## 711                   0.421048777                    0.388045492
## 712                   0.688894460                    0.665439563
## 713                   0.155131190                    0.330233575
## 714                   0.312164638                    0.326821732
## 715                   0.471046275                    0.332591915
## 716                   0.592781972                    0.652649865
## 717                   0.603135905                    0.656954965
## 718                   0.530108625                    0.476497060
## 719                   0.352513492                    0.357230640
## 720                   0.330701975                    0.317525593
## 721                   0.413420867                    0.397920332
## 722                   0.418634847                    0.413547220
## 723                   0.646703025                    0.468055810
## 724                   0.468329597                    0.459999257
## 725                   0.285460995                    0.314189960
## 726                   0.333022550                    0.337234100
## 727                   0.440045097                    0.362971225
## 728                   0.683603907                    0.679544090
## 729                   0.455348797                    0.322902300
## 730                   0.968150200                    0.570728992
## 731                   0.670394382                    0.667231570
## 732                   0.960530525                    0.568090245
## 733                   1.015551375                    0.576674270
## 734                   0.254436245                    0.108107708
## 735                   0.645212007                    0.661454895
## 736                   0.333022550                    0.337234100
## 737                   0.407057625                    0.269329977
## 738                   0.474156050                    0.343521375
## 739                   0.426445550                    0.351783153
## 740                   0.596949203                    0.658815957
## 741                   0.398095200                    0.266183589
## 742                   0.433957625                    0.405480842
## 743                   0.310863550                    0.328386150
## 744                   0.656702300                    0.446942545
## 745                   0.661174650                    0.414714292
## 746                   0.756396670                    0.653843537
## 747                   0.684402428                    0.656537462
## 748                   0.604590712                    0.660912381
## 749                   0.676830765                    0.652317305
## 750                   0.286074705                    0.361339977
## 751                   0.410188200                    0.259046597
## 752                   0.956843950                    0.555045355
## 753                   0.755858743                    0.681438187
## 754                   0.487635225                    0.325790825
## 755                   0.422160875                    0.415840035
## 756                   0.690767022                    0.656522107
## 757                   1.010817100                    0.566074530
## 758                   0.765174475                    0.664895126
## 759                   0.669202250                    0.474651972
## 760                   0.958860750                    0.561929295
## 761                   1.011419825                    0.589646030
## 762                   0.246209655                    0.170885627
## 763                   0.603135905                    0.656954965
## 764                   0.391146017                    0.417173962
## 765                   0.659818925                    0.446890062
## 766                   0.290939167                    0.362208582
## 767                   0.685160160                    0.654742060
## 768                   0.685160160                    0.654742060
## 769                   0.433957625                    0.405480842
## 770                   0.397234452                    0.392454107
## 771                   0.397803630                    0.415411952
## 772                   0.517556300                    0.464052020
## 773                   0.202161342                    0.148352672
## 774                   0.280122225                    0.313098065
## 775                   0.759190052                    0.662463820
## 776                   0.758823152                    0.664427263
## 777                   0.685160160                    0.654742060
## 778                   0.772975677                    0.642204925
## 779                   0.662905900                    0.439199037
## 780                   0.690767022                    0.656522107
## 781                   0.455449200                    0.310772277
## 782                   0.395326431                    0.396062865
## 783                   0.968150200                    0.570728992
## 784                   0.607676187                    0.669072430
## 785                   0.685160160                    0.654742060
## 786                   0.603135905                    0.656954965
## 787                   0.953894050                    0.555471905
## 788                   0.969796850                    0.575448630
## 789                   1.011419825                    0.589646030
## 790                   0.425802970                    0.467661232
## 791                   0.685160160                    0.654742060
## 792                   0.522315575                    0.465430045
## 793                   0.960530525                    0.568090245
## 794                   0.765819340                    0.669634841
## 795                   0.953894050                    0.555471905
## 796                   0.438108250                    0.349575481
## 797                   0.968150200                    0.570728992
## 798                   0.953894050                    0.555471905
## 799                   0.958860750                    0.561929295
## 800                   0.610183632                    0.659179880
## 801                   0.764564800                    0.645567960
## 802                   0.690767022                    0.656522107
## 803                   0.984964100                    0.574502965
## 804                   0.980589475                    0.567818102
## 805                   0.520342750                    0.469479122
## 806                   0.603135905                    0.656954965
## 807                   1.012491550                    0.575020477
## 808                   0.598586535                    0.654982927
## 809                   1.015551375                    0.576674270
## 810                   0.675930345                    0.666100282
## 811                   1.012491550                    0.575020477
## 812                   0.953894050                    0.555471905
## 813                   0.593056925                    0.655023090
##     upper.975_q_hard_skill_winner full_name_loser_loser
## 1                    0.1611020750         Roger Federer
## 2                    0.0774975575          Rafael Nadal
## 3                    0.2594796500        Novak Djokovic
## 4                    0.2531844250       Grigor Dimitrov
## 5                    0.1018258500         Stan Wawrinka
## 6                    0.0680054950     Mikhail Kukushkin
## 7                    0.3597093000        Novak Djokovic
## 8                    0.1450103750         Kei Nishikori
## 9                    0.1988842000         Dominic Thiem
## 10                   0.2917073750           Andy Murray
## 11                   0.4754041750          Rafael Nadal
## 12                   0.4632594750       Richard Gasquet
## 13                   0.0455356925        Jerzy Janowicz
## 14                   0.4558335750          Rafael Nadal
## 15                   0.0329148450 Philipp Kohlschreiber
## 16                   0.3120148000           Andy Murray
## 17                   0.3863883000          Rafael Nadal
## 18                   0.1325168250          David Ferrer
## 19                   0.4323098500        Novak Djokovic
## 20                   0.1419857500       Grigor Dimitrov
## 21                   0.1517387000         Kei Nishikori
## 22                   0.0685101125           Marin Cilic
## 23                   0.1717083250          Milos Raonic
## 24                  -0.0117434725   Alexandr Dolgopolov
## 25                  -0.0023902923            John Isner
## 26                   0.0546993075 Roberto Bautista Agut
## 27                   0.0023369017         Fabio Fognini
## 28                   0.3597093000          Rafael Nadal
## 29                   0.0598288900 Philipp Kohlschreiber
## 30                   0.2182812750          Milos Raonic
## 31                   0.0103087625        Kevin Anderson
## 32                   0.4147583750        Viktor Troicki
## 33                   0.1142768000            John Isner
## 34                   0.1520416750          Gael Monfils
## 35                   0.1871607500         Kei Nishikori
## 36                   0.2648052000         Stan Wawrinka
## 37                   0.0243834750          Milos Raonic
## 38                   0.1187038750       Grigor Dimitrov
## 39                   0.0435766875         Fabio Fognini
## 40                  -0.0250686550     Sergiy Stakhovsky
## 41                   0.2671016750         Stan Wawrinka
## 42                   0.1480152000        Kevin Anderson
## 43                   0.1361751000         Kei Nishikori
## 44                   0.1618620750         Tomas Berdych
## 45                   0.4856415000           Andy Murray
## 46                   0.3465358500         Roger Federer
## 47                   0.2312280500          Rafael Nadal
## 48                   0.1498400250       Nicolas Almagro
## 49                   0.0946157525            John Isner
## 50                   0.2450055500           Marin Cilic
## 51                   0.1411623250       Richard Gasquet
## 52                   0.1242811500         Jeremy Chardy
## 53                   0.2161266750           Sam Querrey
## 54                   0.0788225325       Grigor Dimitrov
## 55                   0.1427213750          David Goffin
## 56                   0.7027772750        Novak Djokovic
## 57                   0.3228627750          David Ferrer
## 58                   0.2377099250           Marin Cilic
## 59                   0.0432857500        Lleyton Hewitt
## 60                   0.0647312450           Sam Querrey
## 61                   0.0381091250            John Isner
## 62                   0.0969050700 Philipp Kohlschreiber
## 63                   0.2336706750         Tomas Berdych
## 64                   0.2363835250       Grigor Dimitrov
## 65                   0.2267072250    Jo-Wilfried Tsonga
## 66                   0.6213505250          Milos Raonic
## 67                   0.3277887250          Gilles Simon
## 68                   0.1403261000        Lleyton Hewitt
## 69                   0.3081665000 Roberto Bautista Agut
## 70                   0.3265473000           Marin Cilic
## 71                   0.1877827500   Alexandr Dolgopolov
## 72                   0.2048046000          Milos Raonic
## 73                   0.1629020500          Gilles Simon
## 74                   0.2834681500       Richard Gasquet
## 75                   0.0531794725       Feliciano Lopez
## 76                   0.1411678500         Fabio Fognini
## 77                   0.2504278500          David Ferrer
## 78                   0.0412210350        Vasek Pospisil
## 79                   0.3447773250    Jo-Wilfried Tsonga
## 80                   0.1603271250          Gilles Simon
## 81                   0.1516064000       Nicolas Almagro
## 82                   0.0839730025         Denis Istomin
## 83                   0.1638391250       Grigor Dimitrov
## 84                  -0.0745665650         Steve Johnson
## 85                   0.3010131250         Stan Wawrinka
## 86                   0.3259429500          Gael Monfils
## 87                   0.2307693250            John Isner
## 88                   0.1362210250        Kevin Anderson
## 89                   0.2203409250       Grigor Dimitrov
## 90                   0.1642311750   Teymuraz Gabashvili
## 91                   0.1478949500         Fabio Fognini
## 92                   0.0808350750 Philipp Kohlschreiber
## 93                   0.6752480750        Novak Djokovic
## 94                  -0.0386064025            John Isner
## 95                   0.6513499750        Novak Djokovic
## 96                   0.3777871250    Jo-Wilfried Tsonga
## 97                  -0.0117434725      Adrian Mannarino
## 98                   0.1618620750          Milos Raonic
## 99                   0.2360081250         Tomas Berdych
## 100                  0.1533887250     Sergiy Stakhovsky
## 101                  0.4432373000         Kei Nishikori
## 102                  0.2190184750         Stan Wawrinka
## 103                  0.3000593000          David Ferrer
## 104                  0.3168163000         Tomas Berdych
## 105                  0.2178971750         Tommy Robredo
## 106                  0.1170266250        Viktor Troicki
## 107                  0.7028012000        Novak Djokovic
## 108                  0.1392636250         Tommy Robredo
## 109                 -0.0714233550         Tommy Robredo
## 110                 -0.0623028575         Pablo Andujar
## 111                  0.3027893250          Milos Raonic
## 112                  0.0596863675        Leonardo Mayer
## 113                  0.1697063750         Bernard Tomic
## 114                  0.1427213750 Philipp Kohlschreiber
## 115                  0.0917376625        Kevin Anderson
## 116                  0.0906073150         Andreas Seppi
## 117                  0.1167688250   Alexandr Dolgopolov
## 118                  0.2190184750        Ernests Gulbis
## 119                  0.6943093750        Novak Djokovic
## 120                  0.0788225325         Jeremy Chardy
## 121                  0.2267072250        Ernests Gulbis
## 122                  0.1393955000        Ernests Gulbis
## 123                  0.1944579500          Milos Raonic
## 124                  0.3277887250        Viktor Troicki
## 125                  0.2404100000         Jurgen Melzer
## 126                  0.0242478875          David Goffin
## 127                  0.2779425250         Kei Nishikori
## 128                  0.2127720750       Mikhail Youzhny
## 129                  0.1144541000 Roberto Bautista Agut
## 130                  0.1245320250           Marin Cilic
## 131                  0.2057885750      Adrian Mannarino
## 132                  0.1493363000       Grigor Dimitrov
## 133                  0.0478108350      Andrey Kuznetsov
## 134                  0.4355769750          Rafael Nadal
## 135                  0.1498400250         Tommy Robredo
## 136                  0.2643548500         Stan Wawrinka
## 137                  0.1716203250            Ivan Dodig
## 138                  0.4035035250       Richard Gasquet
## 139                  0.2243795250         Stan Wawrinka
## 140                  0.1945574000       Dmitry Tursunov
## 141                  0.2606614250         Florian Mayer
## 142                  0.1147559250        Kevin Anderson
## 143                  0.1360004750        Radek Stepanek
## 144                  0.2250766750           Jiri Vesely
## 145                  0.1846010750       Richard Gasquet
## 146                  0.2234529250             Jack Sock
## 147                  0.3267902500 Philipp Kohlschreiber
## 148                  0.1202428750      Adrian Mannarino
## 149                  0.1048354750     Sergiy Stakhovsky
## 150                  0.2475868000         Stan Wawrinka
## 151                  0.0265991000    Matthias Bachinger
## 152                  0.2093307500       Grigor Dimitrov
## 153                  0.1877827500         Martin Klizan
## 154                  0.0945533375 Philipp Kohlschreiber
## 155                  0.1140000250           Sam Querrey
## 156                  0.1427213750          Pablo Cuevas
## 157                  0.2813112500         Fabio Fognini
## 158                  0.1077825000         Tommy Robredo
## 159                  0.1455214500       Mikhail Youzhny
## 160                 -0.0323322225      Santiago Giraldo
## 161                  0.1328159250         Gilles Muller
## 162                  0.0867454800          Benoit Paire
## 163                  0.1092410500         Ryan Harrison
## 164                 -0.1386047000         Paolo Lorenzi
## 165                  0.1698581500        Kevin Anderson
## 166                 -0.0913482200 Philipp Kohlschreiber
## 167                  0.4432373000         Tomas Berdych
## 168                  0.1041819750       Thomaz Bellucci
## 169                  0.6967450750        Novak Djokovic
## 170                 -0.0007427301             Dudi Sela
## 171                  0.0906304050          Ivo Karlovic
## 172                  0.3139817500          David Goffin
## 173                  0.1382924750            Ivan Dodig
## 174                  0.1794033500         Nicolas Mahut
## 175                  0.0988585900          Donald Young
## 176                  0.3061250750            Ivan Dodig
## 177                  0.2594882500         Kei Nishikori
## 178                  0.1041819750   Teymuraz Gabashvili
## 179                  0.3265473000         Daniel Brands
## 180                  0.0474826275      Santiago Giraldo
## 181                  0.2121836500         Ryan Harrison
## 182                  0.2762093250           Marin Cilic
## 183                  0.0581643000       Dmitry Tursunov
## 184                  0.0577589350   Alexandr Dolgopolov
## 185                 -0.0128357250         Fabio Fognini
## 186                  0.2451929500          Gilles Simon
## 187                  0.1516064000         Tommy Robredo
## 188                  0.0919827650       Grigor Dimitrov
## 189                  0.0125170525            Joao Sousa
## 190                  0.1504462500           Sam Querrey
## 191                  0.0197804600         Steve Johnson
## 192                  0.2062814500           Denis Kudla
## 193                  0.1658366000     Mikhail Kukushkin
## 194                  0.2325713000          Milos Raonic
## 195                  0.2356913250           Marin Cilic
## 196                  0.2190184750        Lleyton Hewitt
## 197                  0.0161595025          Donald Young
## 198                  0.3051559750          Steve Darcis
## 199                 -0.0808075000            Joao Sousa
## 200                  0.0563680975           Robin Haase
## 201                  0.1374513000          Benoit Paire
## 202                  0.1697063750         Jeremy Chardy
## 203                  0.3943249250    Jo-Wilfried Tsonga
## 204                  0.2213076250   Alexandr Dolgopolov
## 205                 -0.0375833850     Michal Przysiezny
## 206                  0.3022456250        Ernests Gulbis
## 207                  0.4864553500         Tomas Berdych
## 208                  0.4071532750      Julien Benneteau
## 209                  0.3937698000          Gilles Simon
## 210                  0.2048046000 Roberto Bautista Agut
## 211                  0.4976267250         Kei Nishikori
## 212                  0.1863870500         Steve Johnson
## 213                  0.2552902000   Alexandr Dolgopolov
## 214                  0.2599148250         Kei Nishikori
## 215                  0.1040970500       Albert Montanes
## 216                  0.0959202725      Adrian Mannarino
## 217                  0.1544674750         Bernard Tomic
## 218                  0.1470804500         Jeremy Chardy
## 219                  0.1638391250          David Goffin
## 220                  0.1775621250            John Isner
## 221                  0.3729529000         Stan Wawrinka
## 222                  0.1450103750         Gilles Muller
## 223                  0.0788225325        Andrey Golubev
## 224                  0.1392623250        Carlos Berlocq
## 225                  0.1414151500      Santiago Giraldo
## 226                  0.3063840750          Gilles Simon
## 227                  0.1195198250         Ryan Harrison
## 228                  0.1264605500         Florian Mayer
## 229                  0.0572553575       Jarkko Nieminen
## 230                  0.2874575750         Tommy Robredo
## 231                  0.2274873250        Ernests Gulbis
## 232                  0.3426740750        Ernests Gulbis
## 233                  0.3711261750         Kei Nishikori
## 234                  0.2047314250         Gilles Muller
## 235                  0.1775634750       Thomaz Bellucci
## 236                  0.0482117725         Martin Klizan
## 237                  0.2717999500       Nicolas Almagro
## 238                  0.4096348000       Nicolas Almagro
## 239                  0.0546042825            Joao Souza
## 240                  0.2654092000            John Isner
## 241                  0.6410517750           Andy Murray
## 242                  0.0242478875     Marinko Matosevic
## 243                  0.2217588250        Vasek Pospisil
## 244                  0.1190995500          Pablo Cuevas
## 245                  0.0941785925      Andrey Kuznetsov
## 246                  0.1153125000        Viktor Troicki
## 247                  0.1335018500       Richard Gasquet
## 248                  0.2307693250          Ivo Karlovic
## 249                  0.2042355500           Robin Haase
## 250                  0.1950071500           Sam Querrey
## 251                  0.2275434000         Fabio Fognini
## 252                  0.0301779300          Pablo Cuevas
## 253                  0.1407677000       Mikhail Youzhny
## 254                  0.2377400250     Fernando Verdasco
## 255                  0.1533887250     Ricardas Berankis
## 256                 -0.0920457300         Fabio Fognini
## 257                  0.0978374550        Vasek Pospisil
## 258                  0.2450055500            John Isner
## 259                  0.4074483000    Jo-Wilfried Tsonga
## 260                  0.2363835250          David Goffin
## 261                  0.3120148000          Gael Monfils
## 262                  0.3763157500       Nicolas Almagro
## 263                  0.2823118500         Tommy Robredo
## 264                  0.2813655750            John Isner
## 265                  0.1420945000        Simone Bolelli
## 266                  0.0432857500     Michal Przysiezny
## 267                  0.0581643000         Daniel Brands
## 268                 -0.0355962625     Alex Bogomolov Jr
## 269                  0.0842316050         Jeremy Chardy
## 270                  0.1946933500        Jerzy Janowicz
## 271                  0.2779425250          Milos Raonic
## 272                  0.1775621250          David Goffin
## 273                  0.2845893750            John Isner
## 274                  0.0941244425   Teymuraz Gabashvili
## 275                  0.1001354000             Jack Sock
## 276                  0.1162762500           Lukas Rosol
## 277                  0.2952670250         Denis Istomin
## 278                  0.1666019250           Lukas Rosol
## 279                  0.2206964750          Gilles Simon
## 280                  0.2834681500        Vasek Pospisil
## 281                  0.3110626500          Ivo Karlovic
## 282                  0.2250143250     Sergiy Stakhovsky
## 283                  0.1369086500      Adrian Mannarino
## 284                  0.0117646725         Fabio Fognini
## 285                  0.3234587500 Roberto Bautista Agut
## 286                  0.1778944500       Grigor Dimitrov
## 287                  0.2178971750           Blaz Kavcic
## 288                  0.2022314250 Roberto Bautista Agut
## 289                  0.1137275500       Alejandro Falla
## 290                  0.2499118500         Bernard Tomic
## 291                  0.4025517250    Jo-Wilfried Tsonga
## 292                  0.2725779750   Alexandr Dolgopolov
## 293                  0.6445420000         Kei Nishikori
## 294                  0.1068206250         Denis Istomin
## 295                  0.1444424250        Frank Dancevic
## 296                  0.1369217250        Jerzy Janowicz
## 297                  0.0124672350      Adrian Mannarino
## 298                  0.1265897000     Marcel Granollers
## 299                  0.0381091250     Marcel Granollers
## 300                  0.0631453100         Fabio Fognini
## 301                  0.1255686500         Gilles Muller
## 302                  0.1569797750      Adrian Mannarino
## 303                  0.2336706750         Bernard Tomic
## 304                  0.0919635350          Benoit Paire
## 305                  0.0959202725          Donald Young
## 306                  0.1424938750      Adrian Mannarino
## 307                  0.3410332750 Philipp Kohlschreiber
## 308                  0.1170266250         Fabio Fognini
## 309                  0.0994778625          Pablo Cuevas
## 310                  0.1451627750            Ivan Dodig
## 311                  0.1335512250           Robin Haase
## 312                 -0.0714233550     Marcel Granollers
## 313                  0.1083042000           Lukas Lacko
## 314                  0.0985946350        Leonardo Mayer
## 315                  0.4056759000         Tommy Robredo
## 316                  0.1366806750          Albert Ramos
## 317                  0.0598288900           Robin Haase
## 318                  0.3228627750         Bernard Tomic
## 319                  0.0597709225   Teymuraz Gabashvili
## 320                  0.1748821500       Stephane Robert
## 321                  0.3550633750         Kei Nishikori
## 322                  0.0936804375     Marinko Matosevic
## 323                  0.2779425250       Grigor Dimitrov
## 324                  0.2870454000          Gilles Simon
## 325                  0.2954566250         Gilles Muller
## 326                  0.1508408000       Benjamin Becker
## 327                  0.1427213750         Denis Istomin
## 328                  0.2961454000         Gilles Muller
## 329                  0.2926743500        Ernests Gulbis
## 330                  0.0552663650     Michal Przysiezny
## 331                  0.2978203250         Pablo Andujar
## 332                  0.2531844250          Tobias Kamke
## 333                  0.0923714850         Pablo Andujar
## 334                  0.0949143125       Feliciano Lopez
## 335                  0.2954566250         Bernard Tomic
## 336                 -0.0180009500         Matthew Ebden
## 337                  0.3005503250        Kevin Anderson
## 338                  0.4296427500         Fabio Fognini
## 339                  0.3658792250       Grigor Dimitrov
## 340                  0.0549966050          Donald Young
## 341                  0.2047314250           Lukas Lacko
## 342                  0.3320970250         Bernard Tomic
## 343                  0.3149320000         Martin Klizan
## 344                  0.3729529000       Grigor Dimitrov
## 345                  0.2875841250 Philipp Kohlschreiber
## 346                  0.2500964000            Ivan Dodig
## 347                  0.3878429750         Tommy Robredo
## 348                  0.3414634750        Leonardo Mayer
## 349                  0.2277459500         Daniel Brands
## 350                  0.4069569500       Richard Gasquet
## 351                  0.1284638500        Andrey Golubev
## 352                  0.0959202725       Benjamin Becker
## 353                  0.4452941750           Marin Cilic
## 354                  0.2234529250       Feliciano Lopez
## 355                  0.4527891750    Jo-Wilfried Tsonga
## 356                  0.2200003750       Feliciano Lopez
## 357                  0.2022314250          David Goffin
## 358                  0.2735216250       Feliciano Lopez
## 359                  0.1575207500          Donald Young
## 360                  0.2954566250           Sam Querrey
## 361                  0.1097807000       Dmitry Tursunov
## 362                  0.0596863675      Adrian Mannarino
## 363                  0.2717999500        Leonardo Mayer
## 364                  0.2654092000       Feliciano Lopez
## 365                  0.2632039750          Albert Ramos
## 366                  0.1647533750     Marinko Matosevic
## 367                  0.0894554750        Simone Bolelli
## 368                  0.2254227000        Simone Bolelli
## 369                  0.1547532750         Martin Klizan
## 370                  0.2428290000       Jarkko Nieminen
## 371                  0.3385437250     Sergiy Stakhovsky
## 372                  0.1666019250            Ivan Dodig
## 373                  0.3447902750         Kei Nishikori
## 374                  0.1470804500        Leonardo Mayer
## 375                  0.1588416250      Adrian Mannarino
## 376                  0.0470471825           Tatsuma Ito
## 377                  0.3358382500        Carlos Berlocq
## 378                  0.3045204000          Ivo Karlovic
## 379                  0.2087487500       Albert Montanes
## 380                  0.2539963000         Ryan Harrison
## 381                  0.1428100500     Marcel Granollers
## 382                  0.1193003000      Santiago Giraldo
## 383                  0.1607429250     Marcel Granollers
## 384                  0.3267902500      Santiago Giraldo
## 385                  0.2203441250       Grigor Dimitrov
## 386                  0.3731142500         Fabio Fognini
## 387                  0.1126469500          Donald Young
## 388                  0.1727728000        Andrey Golubev
## 389                  0.3937698000       Jarkko Nieminen
## 390                  0.2235115000        Vasek Pospisil
## 391                  0.2370213000     Mikhail Kukushkin
## 392                  0.0816199975           Lukas Rosol
## 393                  0.2717999500          Pablo Cuevas
## 394                  0.2077435250     Kenny De Schepper
## 395                  0.3276142250          Dustin Brown
## 396                  0.2360081250   Alexandr Dolgopolov
## 397                  0.2523375500     Fernando Verdasco
## 398                  0.1806281750    Matthias Bachinger
## 399                  0.1646231000   Teymuraz Gabashvili
## 400                  0.1162762500           Lukas Lacko
## 401                  0.0424079075      Adrian Mannarino
## 402                  0.1646231000            Joao Sousa
## 403                  0.0799193450   Teymuraz Gabashvili
## 404                  0.2514766250     Mikhail Kukushkin
## 405                  0.2648052000         Andreas Seppi
## 406                  0.1376539500       Benjamin Becker
## 407                  0.3988570250         Kei Nishikori
## 408                  0.3747285250 Roberto Bautista Agut
## 409                  0.0981357575       Alejandro Falla
## 410                  0.2599148250         Jeremy Chardy
## 411                  0.1739466000   Alexandr Dolgopolov
## 412                  0.1904770000        Leonardo Mayer
## 413                  0.2003466250          Marsel Ilhan
## 414                  0.1475195000          Adrian Ungur
## 415                  0.3254028750     Marinko Matosevic
## 416                 -0.0523886650     Marcel Granollers
## 417                  0.0990920900       Stephane Robert
## 418                  0.0304184300        Michael Llodra
## 419                  0.6508987000       Nicolas Almagro
## 420                  0.4354232000   Alexandr Dolgopolov
## 421                  0.0554470525        Leonardo Mayer
## 422                  0.1023366500        Vasek Pospisil
## 423                  0.0474826275       Maximo Gonzalez
## 424                  0.4523488750          Gael Monfils
## 425                  0.2870454000   Alexandr Dolgopolov
## 426                  0.7419930500         Roger Federer
## 427                  0.2981896250        Ernests Gulbis
## 428                  0.2237472000         Jeremy Chardy
## 429                  0.3805248250         Kei Nishikori
## 430                  0.2414821250           Lukas Rosol
## 431                  0.6922870000       Jarkko Nieminen
## 432                  0.1513377000         Paolo Lorenzi
## 433                  0.0577589350          Benoit Paire
## 434                  0.1923891750   Teymuraz Gabashvili
## 435                  0.2654092000         Daniel Brands
## 436                  0.1427084250       Jarkko Nieminen
## 437                  0.3287070500        Victor Hanescu
## 438                  0.2780119250      Julien Benneteau
## 439                  0.3937698000     Marinko Matosevic
## 440                  0.4415757500          David Goffin
## 441                  0.3465358500       Grigor Dimitrov
## 442                  0.2786246250        Vasek Pospisil
## 443                  0.2370213000         Martin Klizan
## 444                  0.2370213000        Simone Bolelli
## 445                  0.1321637750      Santiago Giraldo
## 446                  0.7073518750           Andy Murray
## 447                  0.1185917250            Rajeev Ram
## 448                  0.1854014000       Benjamin Becker
## 449                  0.1896490750      Thiemo De Bakker
## 450                  0.1945574000      Santiago Giraldo
## 451                  0.2813655750         Jeremy Chardy
## 452                  0.1854167500          Steve Darcis
## 453                  0.2370213000         Gilles Muller
## 454                  0.1059519250           Tatsuma Ito
## 455                  0.1944579500         Fabio Fognini
## 456                  0.1427716750        Simone Bolelli
## 457                  0.2684822500             Jack Sock
## 458                  0.2780119250         Jeremy Chardy
## 459                  0.3426740750           Juan Monaco
## 460                  0.3937698000          Donald Young
## 461                  0.2238744250          Donald Young
## 462                  0.6423160500         Stan Wawrinka
## 463                  0.1523608250             Dudi Sela
## 464                  0.0830084725         Matthew Ebden
## 465                  0.0047564495        Vasek Pospisil
## 466                  0.2023132250         Daniel Brands
## 467                  0.3416032250        Kevin Anderson
## 468                  0.2917073750        Kevin Anderson
## 469                  0.4323098500       Grigor Dimitrov
## 470                  0.0992652475   Teymuraz Gabashvili
## 471                  0.1424938750        Frank Dancevic
## 472                  0.1504462500        Leonardo Mayer
## 473                  0.3426740750            Ivan Dodig
## 474                  0.1775889000         Fabio Fognini
## 475                  0.2569072000           Jiri Vesely
## 476                  0.4355769750        Kevin Anderson
## 477                  0.2394423500      Adrian Mannarino
## 478                  0.2363835250   Teymuraz Gabashvili
## 479                  0.6509220750           Marin Cilic
## 480                  0.1577106000          Pablo Cuevas
## 481                  0.2200003750         Bernard Tomic
## 482                  0.3027893250          David Goffin
## 483                  0.2961454000        Vasek Pospisil
## 484                  0.3992118500          Albert Ramos
## 485                  0.2761372250         Fabio Fognini
## 486                  0.2874575750   Teymuraz Gabashvili
## 487                  0.2377400250       Alejandro Falla
## 488                  0.0959202725     Michal Przysiezny
## 489                  0.2773402750         Andreas Seppi
## 490                  0.1056463250           Blaz Kavcic
## 491                  0.6530348750    Jo-Wilfried Tsonga
## 492                  0.4392836500       Grigor Dimitrov
## 493                  0.2370213000        Leonardo Mayer
## 494                  0.0865492950           Jurgen Zopp
## 495                  0.3638006250 Roberto Bautista Agut
## 496                  0.2469190250     Sergiy Stakhovsky
## 497                  0.3907457000            John Isner
## 498                  0.2010471000         Andreas Seppi
## 499                  0.0430744350     Ricardas Berankis
## 500                  0.6423160500           Marin Cilic
## 501                  0.3422290250         Bernard Tomic
## 502                  0.1871607500          Pablo Cuevas
## 503                  0.2556586500     Federico Delbonis
## 504                  0.2372595250         Matthew Ebden
## 505                  0.7027772750         Tomas Berdych
## 506                  0.2008713000         Jeremy Chardy
## 507                  0.3175326750          Dustin Brown
## 508                  0.2773402750       Thomaz Bellucci
## 509                  0.2497271750          Donald Young
## 510                  0.3000593000           Lukas Rosol
## 511                  0.3000593000        Simone Bolelli
## 512                  0.6410517750         Stan Wawrinka
## 513                  0.3259429500           Lukas Rosol
## 514                  0.7473614250         Roger Federer
## 515                  0.2182812750          Pablo Cuevas
## 516                  0.0993530175   Teymuraz Gabashvili
## 517                  0.6353583250        Novak Djokovic
## 518                  0.6438608250         Tomas Berdych
## 519                  0.0949143125     Ricardas Berankis
## 520                  0.2238744250           Lukas Rosol
## 521                  0.2980134250         Gilles Muller
## 522                  0.7190806750          Rafael Nadal
## 523                  0.2020570250        Vasek Pospisil
## 524                  0.6515058500          David Ferrer
## 525                  0.3385437250           Blaz Kavcic
## 526                  0.2449689750         Tommy Robredo
## 527                  0.2238098500        Simone Bolelli
## 528                  0.4323644500       Grigor Dimitrov
## 529                  0.6508987000     Fernando Verdasco
## 530                  0.2355274500      Adrian Mannarino
## 531                  0.1290353000           Jan Hernych
## 532                  0.6513499750         Kei Nishikori
## 533                  0.0943328375           Tatsuma Ito
## 534                  0.3435854500        Carlos Berlocq
## 535                  0.3447773250         Andreas Seppi
## 536                  0.2760565500       Benjamin Becker
## 537                  0.1843013000      Adrian Mannarino
## 538                  0.1396083750            Joao Sousa
## 539                  0.2789332250     Sergiy Stakhovsky
## 540                  0.1605772250      Julien Benneteau
## 541                  0.2475868000         Fabio Fognini
## 542                  0.3658792250 Roberto Bautista Agut
## 543                  0.1686441750        Simone Bolelli
## 544                  0.3743410000          Ivo Karlovic
## 545                  0.1068206250           Lukas Rosol
## 546                  0.2823654250         Jurgen Melzer
## 547                  0.3232131250           Robin Haase
## 548                  0.2493524250        Andrey Golubev
## 549                  0.4767647250            John Isner
## 550                  0.4538253250          Gilles Simon
## 551                  0.1268793500          Pablo Cuevas
## 552                  0.3937698000        Leonardo Mayer
## 553                  0.3330508750        Andrey Golubev
## 554                  0.0371615800     Sergiy Stakhovsky
## 555                  0.3930374750        Leonardo Mayer
## 556                  0.6994908750    Jo-Wilfried Tsonga
## 557                  0.2408653500           Lukas Rosol
## 558                  0.3673722250 Roberto Bautista Agut
## 559                  0.2497271750      Adrian Mannarino
## 560                  0.1725525250         Pablo Andujar
## 561                  0.4986368500       Richard Gasquet
## 562                  0.6303209750         Bernard Tomic
## 563                  0.1407677000         Denis Istomin
## 564                  0.2377099250       Benjamin Becker
## 565                  0.1806281750        Andrey Golubev
## 566                  0.2561513000   Alexandr Dolgopolov
## 567                  0.4061353750          Lukasz Kubot
## 568                  0.0985946350      Filippo Volandri
## 569                  0.2856441500     Sergiy Stakhovsky
## 570                  0.2823654250     Marcel Granollers
## 571                  0.2773402750        Victor Hanescu
## 572                  0.3708462750        Kevin Anderson
## 573                  0.6423160500          Milos Raonic
## 574                  0.1023366500          Donald Young
## 575                  0.2849542750            Joao Sousa
## 576                  0.3987424500         Tommy Robredo
## 577                  0.2497271750          Dustin Brown
## 578                  0.1581415000          Malek Jaziri
## 579                  0.4074483000            Ivan Dodig
## 580                  0.1336150750            Bjorn Phau
## 581                  0.3166530750            Rajeev Ram
## 582                  0.4841488250         Tommy Robredo
## 583                  0.3276142250       Alejandro Falla
## 584                  0.0187015525          Aljaz Bedene
## 585                  0.1188091750       Illya Marchenko
## 586                  0.4538253250       Grigor Dimitrov
## 587                  0.3992118500        Viktor Troicki
## 588                  0.3488531750        Vasek Pospisil
## 589                  0.3027893250            Joao Sousa
## 590                  0.3708462750          Ivo Karlovic
## 591                  0.2287423250           Lukas Lacko
## 592                  0.2274873250          Pablo Cuevas
## 593                  0.4856415000          David Goffin
## 594                  0.0940572025         Paolo Lorenzi
## 595                  0.1159166000         Denis Istomin
## 596                  0.1963409750         Mischa Zverev
## 597                  0.4205046750        Ernests Gulbis
## 598                  0.4096348000      Santiago Giraldo
## 599                  0.3966724000     Marcel Granollers
## 600                 -0.0809341325         Paolo Lorenzi
## 601                  0.6508987000          Gael Monfils
## 602                  0.3230108500         Gilles Muller
## 603                  0.3010131250      Andrey Kuznetsov
## 604                  0.4071532750        Andrey Golubev
## 605                  0.1618620750   Teymuraz Gabashvili
## 606                  0.6515058500       Grigor Dimitrov
## 607                  0.6497985750          Milos Raonic
## 608                  0.2982993500       Benjamin Becker
## 609                  0.2737069750       Alejandro Falla
## 610                  0.4777214500       Feliciano Lopez
## 611                  0.2654092000         Matthew Ebden
## 612                  0.4841488250 Philipp Kohlschreiber
## 613                  0.1420945000       Maximo Gonzalez
## 614                  0.3546097250         Gilles Muller
## 615                  0.3550633750          David Goffin
## 616                  0.3139817500   Teymuraz Gabashvili
## 617                  0.4436990750         Bernard Tomic
## 618                  0.2705073500           Robin Haase
## 619                  0.3691122750           Denis Kudla
## 620                  0.2823118500         Denis Istomin
## 621                  0.1367850250   Teymuraz Gabashvili
## 622                  0.7056374500         Kei Nishikori
## 623                  0.2377099250           Lukas Rosol
## 624                  0.2762093250   Teymuraz Gabashvili
## 625                  0.4025517250         Jeremy Chardy
## 626                  0.2231995500            Joao Sousa
## 627                  0.4538253250             Jack Sock
## 628                  0.2243795250         Fabio Fognini
## 629                  0.3254028750         Ryan Harrison
## 630                  0.4856415000         Martin Klizan
## 631                  0.2453308750           Lukas Rosol
## 632                  0.2593561750          Donald Young
## 633                  0.6423160500             Jack Sock
## 634                  0.6423160500         Fabio Fognini
## 635                  0.6423160500       Grigor Dimitrov
## 636                  0.7053962250         Kei Nishikori
## 637                  0.4432373000           Sam Querrey
## 638                  0.3000593000          Donald Young
## 639                  0.1309370000            Joao Sousa
## 640                  0.4375622500         Gilles Muller
## 641                  0.3743410000         Gilles Muller
## 642                  0.2630344750       Benjamin Becker
## 643                  0.2151536250         Jeremy Chardy
## 644                  0.4752543500        Ernests Gulbis
## 645                  0.3358382500      Filippo Volandri
## 646                  0.1705611250         Paolo Lorenzi
## 647                  0.3988570250       Feliciano Lopez
## 648                  0.7073518750          Milos Raonic
## 649                  0.0631453100           Guido Pella
## 650                  0.2472479000   Teymuraz Gabashvili
## 651                  0.2536467250        Leonardo Mayer
## 652                  0.1235898250   Rogerio Dutra Silva
## 653                  0.6423160500          Ivo Karlovic
## 654                  0.2594882500         Fabio Fognini
## 655                  0.6508987000 Philipp Kohlschreiber
## 656                  0.3680411750         Tommy Robredo
## 657                  0.1416217000     Michal Przysiezny
## 658                  0.1837015750   Teymuraz Gabashvili
## 659                  0.2773402750       Jarkko Nieminen
## 660                  0.6530348750            John Isner
## 661                  0.2770072500      Andrey Kuznetsov
## 662                  0.2632039750      Horacio Zeballos
## 663                  0.2730772000       Alejandro Falla
## 664                  0.7056374500          Milos Raonic
## 665                  0.4856415000          Ivo Karlovic
## 666                  0.3905537500   Teymuraz Gabashvili
## 667                  0.2370213000         Pablo Andujar
## 668                  0.3022456250      Santiago Giraldo
## 669                  0.4395734750       Feliciano Lopez
## 670                  0.4526618500         Fabio Fognini
## 671                  0.1588416250   Teymuraz Gabashvili
## 672                  0.2913426000       Michael Russell
## 673                 -0.0218966250      Adrian Mannarino
## 674                  0.2235115000         Pablo Andujar
## 675                  0.4864553500          Ivo Karlovic
## 676                  0.3120148000            Joao Sousa
## 677                  0.2717999500       Jarkko Nieminen
## 678                  0.6513499750       Richard Gasquet
## 679                  0.3982496500         Steve Johnson
## 680                  0.3503383750          Steve Darcis
## 681                  0.4754041750       Grigor Dimitrov
## 682                  0.4069569500          Pablo Cuevas
## 683                  0.3610570500            Joao Sousa
## 684                  0.3890290750         Paolo Lorenzi
## 685                  0.2356448500       Illya Marchenko
## 686                  0.6337854250          David Ferrer
## 687                  0.4432373000           Lukas Rosol
## 688                  0.2226172000            Rajeev Ram
## 689                  0.3447902750             Dudi Sela
## 690                 -0.0913482200      Adrian Mannarino
## 691                  0.3729529000        Simone Bolelli
## 692                  0.2185952500         Pablo Andujar
## 693                  0.3982496500          Donald Young
## 694                  0.4707684250         Jeremy Chardy
## 695                  0.4723396000         Fabio Fognini
## 696                  0.4752543500        Ernests Gulbis
## 697                  0.2578293750       Stephane Robert
## 698                  0.2773402750        Andrey Golubev
## 699                  0.4841488250            Ivan Dodig
## 700                  0.7073518750          Gael Monfils
## 701                  0.4841488250      Julien Benneteau
## 702                  0.3503383750        Simone Bolelli
## 703                  0.4976267250         Bernard Tomic
## 704                  0.3773756500   Teymuraz Gabashvili
## 705                  0.2213076250         Igor Sijsling
## 706                  0.2219527000          Marsel Ilhan
## 707                  0.1237310750   Teymuraz Gabashvili
## 708                  0.4538253250             Jack Sock
## 709                  0.6893981000          Gael Monfils
## 710                  0.2881612250        Simone Bolelli
## 711                  0.3422290250         Martin Klizan
## 712                  0.7053962250          Milos Raonic
## 713                  0.2360081250           Tatsuma Ito
## 714                  0.2994969500   Rogerio Dutra Silva
## 715                  0.4096348000          Donald Young
## 716                  0.6508987000     Marcel Granollers
## 717                  0.6515058500      Julien Benneteau
## 718                  0.4409298750         Bernard Tomic
## 719                  0.3494676000           Lukas Rosol
## 720                  0.2823118500         Denis Istomin
## 721                  0.3987424500     Mikhail Kukushkin
## 722                  0.3691891750          Ivo Karlovic
## 723                  0.4986368500           Marin Cilic
## 724                  0.4436990750          Benoit Paire
## 725                  0.3225451750          Donald Young
## 726                  0.2630344750      Horacio Zeballos
## 727                  0.4061106000             Dudi Sela
## 728                  0.7056374500         Stan Wawrinka
## 729                  0.3890290750       Maximo Gonzalez
## 730                  0.6265284250         Tomas Berdych
## 731                  0.7022325000   Alexandr Dolgopolov
## 732                  0.6410517750        Kevin Anderson
## 733                  0.6259777500        Kevin Anderson
## 734                  0.1065575500       Illya Marchenko
## 735                  0.6887062500         Stan Wawrinka
## 736                  0.2630344750         Wayne Odesnik
## 737                  0.2823654250       Benjamin Becker
## 738                  0.4069569500        Michael Llodra
## 739                  0.3602374000     Marinko Matosevic
## 740                  0.6509220750         Tommy Robredo
## 741                  0.2849542750         Paolo Lorenzi
## 742                  0.3574118000        Simone Bolelli
## 743                  0.2761372250           Lukas Rosol
## 744                  0.4777214500     Mikhail Kukushkin
## 745                  0.4752543500            John Isner
## 746                  0.7173325250       Grigor Dimitrov
## 747                  0.6968265500       Grigor Dimitrov
## 748                  0.6438608250       Grigor Dimitrov
## 749                  0.6922870000          Pablo Cuevas
## 750                  0.3456450000       Benjamin Becker
## 751                  0.2773402750             Pere Riba
## 752                  0.6274278500         Jeremy Chardy
## 753                  0.7473614250         Stan Wawrinka
## 754                  0.4035035250      Horacio Zeballos
## 755                  0.3435854500         Bernard Tomic
## 756                  0.7073518750          Gael Monfils
## 757                  0.6257746500        Simone Bolelli
## 758                  0.7419541750         Stan Wawrinka
## 759                  0.4976267250         Fabio Fognini
## 760                  0.6423160500        Vasek Pospisil
## 761                  0.6353583250       Grigor Dimitrov
## 762                  0.1414151500      Adrian Mannarino
## 763                  0.6515058500         Tommy Robredo
## 764                  0.3982496500      Andrey Kuznetsov
## 765                  0.4750009750         Fabio Fognini
## 766                  0.3486657250     Michal Przysiezny
## 767                  0.6943093750          Gilles Simon
## 768                  0.6943093750       Grigor Dimitrov
## 769                  0.3574118000         Pablo Andujar
## 770                  0.3907457000         Mischa Zverev
## 771                  0.4025517250            Joao Sousa
## 772                  0.4395734750         Martin Klizan
## 773                  0.1309370000   Rogerio Dutra Silva
## 774                  0.2895620500         Pablo Andujar
## 775                  0.7357494250         Kei Nishikori
## 776                  0.7312100250       Grigor Dimitrov
## 777                  0.6943093750          David Goffin
## 778                  0.7190806750            John Isner
## 779                  0.4756286000         Pablo Andujar
## 780                  0.7073518750       Feliciano Lopez
## 781                  0.3905537500              Go Soeda
## 782                  0.3836162000            Joao Sousa
## 783                  0.6265284250       Grigor Dimitrov
## 784                  0.6441618000       Feliciano Lopez
## 785                  0.6943093750      Julien Benneteau
## 786                  0.6515058500        Vasek Pospisil
## 787                  0.6222903750         Fabio Fognini
## 788                  0.6231593500   Alexandr Dolgopolov
## 789                  0.6353583250           Andy Murray
## 790                  0.4328850250            Jimmy Wang
## 791                  0.6943093750 Roberto Bautista Agut
## 792                  0.4392836500      Adrian Mannarino
## 793                  0.6410517750           Lukas Rosol
## 794                  0.7492505000            John Isner
## 795                  0.6222903750          Pablo Cuevas
## 796                  0.3703772250            Joao Sousa
## 797                  0.6265284250            John Isner
## 798                  0.6222903750     Fernando Verdasco
## 799                  0.6423160500           Lukas Rosol
## 800                  0.6529283500       Feliciano Lopez
## 801                  0.7180429500        Ernests Gulbis
## 802                  0.7073518750        Vasek Pospisil
## 803                  0.6276965250          Donald Young
## 804                  0.6337854250            John Isner
## 805                  0.4354145000   Teymuraz Gabashvili
## 806                  0.6515058500         Fabio Fognini
## 807                  0.6302150750           Juan Monaco
## 808                  0.6497634750         Pablo Andujar
## 809                  0.6259777500             Dudi Sela
## 810                  0.7027772750           Lukas Rosol
## 811                  0.6302150750        Carlos Berlocq
## 812                  0.6222903750         Andreas Seppi
## 813                  0.6530348750    Matthias Bachinger
##     posterior_mean_clay_skill_loser posterior_mean_grass_skill_loser
## 1                      0.5807562724                      0.536094157
## 2                      0.8390065205                      0.465491652
## 3                      0.6840091204                      0.596275429
## 4                      0.0088523099                      0.113491680
## 5                      0.3362028910                      0.237053044
## 6                     -0.0459825000                      0.015723887
## 7                      0.6560474117                      0.518789519
## 8                      0.2603510744                      0.151842236
## 9                      0.0949217508                      0.013114518
## 10                     0.4832169255                      0.524956064
## 11                     0.8777740180                      0.445617335
## 12                     0.3563865532                      0.283905940
## 13                     0.1596262746                      0.181707049
## 14                     0.8600008865                      0.449520215
## 15                     0.2301551860                      0.217253640
## 16                     0.4873114074                      0.559663418
## 17                     0.8939345095                      0.458609035
## 18                     0.5837723528                      0.332598698
## 19                     0.6623145614                      0.560524841
## 20                     0.0959324252                      0.126857704
## 21                     0.2162675539                      0.075617733
## 22                     0.3011973375                      0.283783864
## 23                     0.2543019420                      0.250257439
## 24                     0.1477056159                      0.142796207
## 25                     0.1787422794                      0.190951515
## 26                    -0.0247867364                     -0.051212765
## 27                     0.0131633296                     -0.124313386
## 28                     0.8654211083                      0.445646853
## 29                     0.2301551860                      0.217253640
## 30                     0.2703080879                      0.236097089
## 31                     0.1909138037                      0.157075029
## 32                     0.1434552932                      0.111972698
## 33                     0.1789298629                      0.198925579
## 34                     0.2215189103                      0.230934812
## 35                     0.2299071679                      0.162234662
## 36                     0.3406514911                      0.223695495
## 37                     0.2551828875                      0.256085001
## 38                     0.1883849726                      0.133488006
## 39                     0.0198209273                     -0.163033146
## 40                    -0.1203983730                      0.080506737
## 41                     0.2967708194                      0.228606727
## 42                     0.1404249879                      0.137041328
## 43                     0.2678689828                      0.164678322
## 44                     0.3504567267                      0.368491520
## 45                     0.4886570410                      0.553972373
## 46                     0.5851355864                      0.557885108
## 47                     0.8741125650                      0.453609325
## 48                     0.3342272415                      0.081544599
## 49                     0.1856364211                      0.179390818
## 50                     0.3068867054                      0.248165246
## 51                     0.3186459235                      0.244567321
## 52                     0.1326593450                      0.079776058
## 53                     0.1174801014                      0.244258124
## 54                     0.1869487443                      0.128288159
## 55                     0.1029040138                      0.009912879
## 56                     0.6594600348                      0.519814702
## 57                     0.5856971979                      0.350553284
## 58                     0.3169074672                      0.280510715
## 59                     0.1820510805                      0.306860523
## 60                     0.1124601432                      0.241038896
## 61                     0.1795616846                      0.198609152
## 62                     0.2343870535                      0.186770147
## 63                     0.4102517657                      0.370868330
## 64                     0.0936397019                      0.119675068
## 65                     0.3022898289                      0.345027355
## 66                     0.2780273041                      0.235112823
## 67                     0.2189431483                      0.179761813
## 68                     0.1874586386                      0.312362021
## 69                    -0.1143985908                     -0.071460351
## 70                     0.3067660291                      0.243829669
## 71                     0.1457987311                      0.120560201
## 72                     0.2485577632                      0.261192392
## 73                     0.2289840966                      0.190059914
## 74                     0.3271929947                      0.262483848
## 75                     0.1485378907                      0.146091964
## 76                     0.0477003034                     -0.070698927
## 77                     0.5863125973                      0.345033723
## 78                    -0.0516232592                     -0.028314916
## 79                     0.3244381066                      0.355410800
## 80                     0.1759333848                      0.191796313
## 81                     0.3587210129                      0.138926741
## 82                    -0.0396351437                      0.138404394
## 83                     0.0959324252                      0.126857704
## 84                    -0.0338500813                     -0.052437436
## 85                     0.3582456488                      0.240087845
## 86                     0.2523152619                      0.242875550
## 87                     0.1778466003                      0.217692483
## 88                     0.1480988146                      0.136820269
## 89                     0.0957139528                      0.122417238
## 90                    -0.0403459700                     -0.114711801
## 91                     0.0025800271                     -0.164760654
## 92                     0.2246999079                      0.227105335
## 93                     0.6759660846                      0.593742115
## 94                     0.1808454468                      0.191701222
## 95                     0.6663057026                      0.583172083
## 96                     0.3786674076                      0.365065770
## 97                    -0.2327086768                     -0.049426858
## 98                     0.2227410412                      0.267199327
## 99                     0.4126867861                      0.367371942
## 100                   -0.0966659530                      0.076882946
## 101                    0.2147608458                      0.162259519
## 102                    0.3357626095                      0.233821097
## 103                    0.5824866445                      0.361894413
## 104                    0.4267340701                      0.351689894
## 105                    0.2440142327                      0.052961861
## 106                    0.1475152157                      0.111124531
## 107                    0.6603813732                      0.528089431
## 108                    0.2442198325                      0.047893252
## 109                    0.2447034979                      0.045640550
## 110                    0.0501582127                     -0.245644087
## 111                    0.2694146711                      0.264478148
## 112                    0.1263675172                     -0.032251189
## 113                   -0.0669573719                      0.134617852
## 114                    0.2290544552                      0.218894041
## 115                    0.1243103738                      0.151087697
## 116                    0.1551044664                      0.060265508
## 117                    0.1526245466                      0.130606344
## 118                    0.1421961514                      0.058457248
## 119                    0.6655238929                      0.560812151
## 120                    0.1302480547                      0.086346658
## 121                    0.1997431989                      0.019668664
## 122                    0.1794281174                      0.036147063
## 123                    0.2716245178                      0.226308266
## 124                    0.1434552932                      0.111972698
## 125                    0.1954825285                      0.161416369
## 126                    0.1355761562                      0.064627449
## 127                    0.2299071679                      0.162234662
## 128                    0.1848026796                      0.223260607
## 129                   -0.0247867364                     -0.051212765
## 130                    0.3149651302                      0.280959188
## 131                   -0.2397809140                     -0.099316812
## 132                    0.1658569195                      0.135673404
## 133                   -0.1000998013                     -0.079291678
## 134                    0.8795784370                      0.452286995
## 135                    0.2432108759                      0.047389840
## 136                    0.3711449565                      0.238573648
## 137                   -0.0728385592                      0.049198406
## 138                    0.2858512839                      0.259047752
## 139                    0.2967708194                      0.228606727
## 140                   -0.1283376684                      0.044440711
## 141                    0.1650340083                      0.146839335
## 142                    0.1909138037                      0.157075029
## 143                    0.1746411435                      0.202774930
## 144                   -0.1193808785                     -0.161867176
## 145                    0.3336747689                      0.298259445
## 146                    0.0603672676                     -0.028303793
## 147                    0.2250410537                      0.190502961
## 148                   -0.2064147248                     -0.087811193
## 149                   -0.0966659530                      0.076882946
## 150                    0.3357626095                      0.233821097
## 151                    0.0070465650                     -0.084992977
## 152                    0.0985276754                      0.137119173
## 153                    0.0284870691                     -0.104949686
## 154                    0.2246999079                      0.227105335
## 155                    0.1175492572                      0.241279605
## 156                    0.0759994140                     -0.069675751
## 157                    0.0048162164                     -0.129386656
## 158                    0.2447034979                      0.045640550
## 159                    0.1847848729                      0.232044476
## 160                    0.1209264674                      0.023539032
## 161                   -0.0566048114                      0.065745338
## 162                    0.0767962039                      0.060009024
## 163                    0.0044429835                      0.051957546
## 164                   -0.1718401445                     -0.234455718
## 165                    0.1427652052                      0.130774714
## 166                    0.2112240303                      0.217794085
## 167                    0.4075669663                      0.362039312
## 168                    0.1539175778                      0.024336549
## 169                    0.6661392277                      0.570674820
## 170                   -0.2103968113                      0.104637883
## 171                    0.0453029172                      0.210124637
## 172                    0.1355761562                      0.064627449
## 173                   -0.0078891431                      0.050735888
## 174                    0.1743381309                      0.092903948
## 175                   -0.2568100701                     -0.076478159
## 176                   -0.0222497278                      0.063112742
## 177                    0.2678689828                      0.164678322
## 178                   -0.0273078089                     -0.125485042
## 179                   -0.1584566285                     -0.046724848
## 180                    0.1211613473                      0.024170554
## 181                   -0.0583285355                      0.068246638
## 182                    0.3168917375                      0.276619304
## 183                   -0.1539577934                      0.079663764
## 184                    0.1460244483                      0.120273595
## 185                    0.0256270432                     -0.072837826
## 186                    0.2272530986                      0.184312705
## 187                    0.2276008428                      0.036419525
## 188                    0.1013943940                      0.140251218
## 189                   -0.1284406518                     -0.179607163
## 190                    0.1167572542                      0.245221298
## 191                   -0.0352932846                     -0.059477191
## 192                   -0.0695317970                      0.073595177
## 193                   -0.0422039527                      0.022523596
## 194                    0.2716245178                      0.226308266
## 195                    0.3118524178                      0.284561561
## 196                    0.1900552145                      0.297573800
## 197                   -0.2611658281                     -0.078004267
## 198                   -0.0260098056                      0.044770274
## 199                   -0.1601876401                     -0.190171005
## 200                    0.0957663060                      0.053104730
## 201                   -0.0142455908                      0.040268629
## 202                    0.1340422301                      0.081863913
## 203                    0.3184825769                      0.363883125
## 204                    0.1640934111                      0.135360180
## 205                   -0.2496297411                     -0.123683190
## 206                    0.1962469400                      0.017863359
## 207                    0.4286444809                      0.356657173
## 208                    0.0200118218                      0.135827416
## 209                    0.2272530986                      0.184312705
## 210                   -0.2325863610                     -0.216418074
## 211                    0.2270828303                      0.153675842
## 212                   -0.0338500813                     -0.052437436
## 213                    0.1343654765                      0.116747226
## 214                    0.1629335425                      0.082192182
## 215                    0.1637497190                     -0.087292681
## 216                   -0.2042571834                     -0.092547890
## 217                   -0.0626783795                      0.123027813
## 218                    0.1340422301                      0.081863913
## 219                    0.1293123803                      0.061038389
## 220                    0.1781801573                      0.188524083
## 221                    0.3711449565                      0.238573648
## 222                   -0.0569359404                      0.064418347
## 223                   -0.0370527358                     -0.046266584
## 224                    0.1262374592                     -0.014107589
## 225                    0.1248047029                      0.029326250
## 226                    0.2257967397                      0.183508598
## 227                   -0.0182281796                      0.030940663
## 228                    0.2126419745                      0.140837124
## 229                    0.0452156735                      0.098928093
## 230                    0.2424123874                      0.047020232
## 231                    0.1474708206                      0.068194532
## 232                    0.1471906976                      0.073692720
## 233                    0.2262340061                      0.147522126
## 234                    0.0093717845                      0.061367575
## 235                    0.1838858451                      0.025568889
## 236                    0.0454363596                      0.021421834
## 237                    0.3603100033                      0.135365405
## 238                    0.3342272415                      0.081544599
## 239                   -0.0858103083                     -0.172980789
## 240                    0.1515285273                      0.176691818
## 241                    0.4617538514                      0.577581675
## 242                   -0.0200908633                     -0.105783623
## 243                   -0.0627248764                     -0.048699369
## 244                    0.0944876466                     -0.061637022
## 245                   -0.1399117788                     -0.078807709
## 246                    0.1475152157                      0.111124531
## 247                    0.3336747689                      0.298259445
## 248                    0.0218408761                      0.197465957
## 249                    0.1292725689                      0.056354398
## 250                    0.1202251063                      0.244364509
## 251                    0.0011017971                     -0.167447661
## 252                    0.1007049791                     -0.083684756
## 253                    0.1792151154                      0.240895329
## 254                    0.3817584166                      0.215007603
## 255                    0.0702361114                      0.065418945
## 256                    0.0382361124                     -0.066757957
## 257                   -0.0038354997                      0.043180270
## 258                    0.1780667325                      0.176014393
## 259                    0.3024502259                      0.337460133
## 260                    0.1151811739                      0.048060980
## 261                    0.2465398419                      0.228410383
## 262                    0.3587210129                      0.138926741
## 263                    0.2424123874                      0.047020232
## 264                    0.1789298629                      0.198925579
## 265                    0.0065593883                     -0.064881211
## 266                   -0.2481048554                     -0.118897889
## 267                   -0.1578824244                     -0.048531941
## 268                   -0.0267769067                      0.038628016
## 269                    0.1187821175                      0.064336540
## 270                    0.0554731457                      0.173969966
## 271                    0.2545247176                      0.262841011
## 272                    0.1285839541                      0.019906182
## 273                    0.1771189417                      0.207153738
## 274                   -0.0279045413                     -0.132029510
## 275                    0.0602478567                     -0.038788307
## 276                   -0.0365237090                     -0.100909954
## 277                   -0.0723693678                      0.158044813
## 278                    0.0206624901                     -0.116896563
## 279                    0.2205937486                      0.176912094
## 280                   -0.0445620435                     -0.024508628
## 281                    0.0389840625                      0.212801582
## 282                   -0.1003690787                      0.073911939
## 283                   -0.2180111389                     -0.024723935
## 284                    0.1139917158                     -0.061310892
## 285                   -0.0937617187                     -0.051447400
## 286                   -0.0126644348                      0.103214130
## 287                   -0.0401500319                     -0.170691781
## 288                   -0.0111753781                     -0.054680682
## 289                    0.0147193373                     -0.030244375
## 290                   -0.0583138542                      0.135509805
## 291                    0.3786674076                      0.365065770
## 292                    0.1306203442                      0.146069429
## 293                    0.2147608458                      0.162259519
## 294                   -0.0855397579                      0.125786351
## 295                   -0.1367120999                     -0.006358633
## 296                    0.0555706734                      0.169525587
## 297                   -0.2416562831                     -0.093893105
## 298                    0.0295590678                      0.116894954
## 299                    0.0295590678                      0.116894954
## 300                    0.0288125833                     -0.078169054
## 301                    0.0131810925                      0.062109846
## 302                   -0.2362909976                     -0.094849388
## 303                   -0.0735383412                      0.180795263
## 304                   -0.0378735176                      0.071527867
## 305                   -0.2618628914                     -0.073244114
## 306                   -0.2416562831                     -0.093893105
## 307                    0.2305328446                      0.222374005
## 308                    0.0683357296                     -0.068249950
## 309                    0.0760235637                     -0.074273674
## 310                   -0.0001539327                      0.048152627
## 311                    0.1358106674                      0.024054388
## 312                    0.0291183168                      0.140723181
## 313                   -0.2511076050                      0.056772093
## 314                    0.1151604585                     -0.027088414
## 315                    0.2432108759                      0.047389840
## 316                    0.1022465321                     -0.039279019
## 317                    0.1290457163                      0.044746906
## 318                   -0.0583138542                      0.135509805
## 319                   -0.0241568965                     -0.115943783
## 320                   -0.2470363067                     -0.135508075
## 321                    0.2262340061                      0.147522126
## 322                   -0.0253299174                     -0.106134748
## 323                    0.0985276754                      0.137119173
## 324                    0.2147493428                      0.181987619
## 325                   -0.0566048114                      0.065745338
## 326                   -0.1593856745                      0.101480602
## 327                   -0.0855347762                      0.144968234
## 328                   -0.0607138473                      0.063707718
## 329                    0.1997431989                      0.019668664
## 330                   -0.2454917165                     -0.118467702
## 331                    0.0679899125                     -0.248514157
## 332                   -0.0383026454                      0.032245260
## 333                    0.0501582127                     -0.245644087
## 334                    0.1448561255                      0.146955652
## 335                   -0.0527729762                      0.176804870
## 336                    0.0048367237                      0.033070694
## 337                    0.1357540867                      0.127260612
## 338                    0.0025800271                     -0.164760654
## 339                    0.0936397019                      0.119675068
## 340                   -0.0696842688                     -0.050989513
## 341                   -0.2826263014                      0.020718443
## 342                   -0.0570642768                      0.157625924
## 343                    0.0895623341                     -0.001760735
## 344                    0.1658569195                      0.135673404
## 345                    0.2242141260                      0.186846641
## 346                   -0.0068349285                      0.048785364
## 347                    0.2432108759                      0.047389840
## 348                    0.1210781788                     -0.033485180
## 349                   -0.1578824244                     -0.048531941
## 350                    0.3195945369                      0.249230005
## 351                   -0.0538435701                     -0.052504558
## 352                   -0.0955048586                      0.099084216
## 353                    0.3187712702                      0.284658543
## 354                    0.1252330882                      0.177297661
## 355                    0.3774534945                      0.364704741
## 356                    0.1420989442                      0.136723613
## 357                    0.1021486137                      0.017993060
## 358                    0.1319186766                      0.144857219
## 359                   -0.2410882252                     -0.071020051
## 360                    0.1165104620                      0.234404640
## 361                   -0.1633302588                      0.077756245
## 362                   -0.2407844420                     -0.089322073
## 363                    0.1241345805                     -0.037393057
## 364                    0.1459951794                      0.158630303
## 365                    0.0504934920                     -0.106918819
## 366                   -0.0252046727                     -0.098649765
## 367                    0.0040419068                     -0.056321510
## 368                    0.0194115978                     -0.063070850
## 369                    0.0831382244                     -0.003243485
## 370                    0.0642736596                      0.089623013
## 371                   -0.0872661129                      0.074746518
## 372                   -0.0615043228                      0.054397098
## 373                    0.2069313527                      0.127156118
## 374                    0.1270231908                     -0.033744725
## 375                   -0.2253909111                     -0.034360806
## 376                   -0.2143555513                     -0.149433186
## 377                    0.1466328218                     -0.017096240
## 378                    0.0312537810                      0.201324546
## 379                    0.1443428373                     -0.079477091
## 380                   -0.0154410819                      0.035976655
## 381                    0.0291183168                      0.140723181
## 382                    0.1199114521                      0.024790330
## 383                    0.0291183168                      0.140723181
## 384                    0.1233057218                      0.029217358
## 385                   -0.0007317147                      0.118179712
## 386                    0.0198209273                     -0.163033146
## 387                   -0.2751233850                     -0.056008588
## 388                   -0.0507449459                     -0.052424524
## 389                    0.0331526702                      0.062061265
## 390                   -0.0649235274                     -0.047597542
## 391                   -0.0254578399                      0.023496547
## 392                    0.0513435988                     -0.017467038
## 393                    0.0969691750                     -0.064008071
## 394                   -0.0604751047                     -0.030840008
## 395                    0.0244622063                     -0.057500251
## 396                    0.1474624093                      0.137416459
## 397                    0.3398501608                      0.241001238
## 398                    0.0098888088                     -0.080030457
## 399                   -0.0273078089                     -0.125485042
## 400                   -0.2511076050                      0.056772093
## 401                   -0.2397809140                     -0.099316812
## 402                   -0.1251437754                     -0.179884725
## 403                   -0.0349839849                     -0.115521733
## 404                   -0.0565439230                      0.083554879
## 405                    0.1591217813                      0.054871917
## 406                   -0.0955048586                      0.099084216
## 407                    0.2112398505                      0.135113954
## 408                   -0.0111753781                     -0.054680682
## 409                    0.0138399478                     -0.014999248
## 410                    0.1237199635                      0.081897105
## 411                    0.1457987311                      0.120560201
## 412                    0.1255584156                     -0.022825230
## 413                   -0.0184241156                     -0.078036377
## 414                   -0.1977468045                     -0.106908026
## 415                   -0.0201646070                     -0.098798990
## 416                    0.0275550567                      0.119994881
## 417                   -0.2424545586                     -0.119037105
## 418                   -0.0776383303                      0.262345023
## 419                    0.3620848637                      0.081266774
## 420                    0.1457987311                      0.120560201
## 421                    0.1209322202                     -0.035816325
## 422                   -0.0395263154                      0.009856052
## 423                   -0.0534830317                     -0.221093664
## 424                    0.2462339222                      0.228186223
## 425                    0.1474624093                      0.137416459
## 426                    0.5764290893                      0.560311150
## 427                    0.2056907272                      0.102537179
## 428                    0.1326593450                      0.079776058
## 429                    0.2109345524                      0.096659364
## 430                   -0.0180715149                     -0.153721005
## 431                    0.0400739293                      0.079636602
## 432                   -0.0991184841                     -0.148922891
## 433                   -0.0524816786                     -0.042307643
## 434                   -0.0440826497                     -0.108494941
## 435                   -0.1578824244                     -0.048531941
## 436                    0.0452156735                      0.098928093
## 437                    0.0841985560                     -0.023462649
## 438                    0.0406634777                      0.128945584
## 439                   -0.0163294430                     -0.095068098
## 440                    0.1111374545                      0.020717485
## 441                    0.1013943940                      0.140251218
## 442                   -0.0232396536                      0.021049456
## 443                    0.0511123249                      0.035446307
## 444                    0.0043561268                     -0.059746715
## 445                    0.1209264674                      0.023539032
## 446                    0.4880022418                      0.556014976
## 447                   -0.1800749200                     -0.028246597
## 448                   -0.0956642560                      0.104430923
## 449                    0.0463216538                      0.039356849
## 450                    0.1240569734                      0.015215122
## 451                    0.1256197846                      0.082894878
## 452                   -0.0406219929                      0.061457638
## 453                    0.0158952433                      0.063610707
## 454                   -0.1809941413                     -0.128453255
## 455                    0.1122767240                     -0.062732416
## 456                    0.0190436166                     -0.084830488
## 457                    0.0602478567                     -0.038788307
## 458                    0.1089464025                      0.072207208
## 459                    0.3210444119                      0.141027043
## 460                   -0.2568100701                     -0.076478159
## 461                   -0.2410882252                     -0.071020051
## 462                    0.3760434845                      0.244821168
## 463                   -0.2262362040                      0.071820027
## 464                   -0.0549831299                     -0.016383462
## 465                   -0.0649235274                     -0.047597542
## 466                   -0.1565345922                     -0.036252402
## 467                    0.1272045704                      0.142661026
## 468                    0.1431753117                      0.133351293
## 469                    0.0936397019                      0.119675068
## 470                   -0.0250933951                     -0.123000678
## 471                   -0.1308233239                     -0.031462754
## 472                    0.1044037648                     -0.027461563
## 473                   -0.0728662032                      0.045549720
## 474                    0.1132836314                     -0.059418750
## 475                   -0.0075733995                     -0.005010503
## 476                    0.1909138037                      0.157075029
## 477                   -0.2064147248                     -0.087811193
## 478                   -0.0112333154                     -0.105749754
## 479                    0.3150384789                      0.282364636
## 480                    0.0754275188                     -0.073301154
## 481                   -0.0680794845                      0.152220912
## 482                    0.1021486137                      0.017993060
## 483                   -0.0204557100                      0.007600339
## 484                    0.0871472020                     -0.080335606
## 485                    0.1122767240                     -0.062732416
## 486                   -0.0367337287                     -0.112157092
## 487                    0.0513360673                     -0.032879266
## 488                   -0.2457501410                     -0.141592045
## 489                    0.1554772666                      0.065142155
## 490                   -0.0384785194                     -0.155652115
## 491                    0.3244381066                      0.355410800
## 492                    0.0957139528                      0.122417238
## 493                    0.1270231908                     -0.033744725
## 494                   -0.0239936403                     -0.097053650
## 495                   -0.1032969791                     -0.058268021
## 496                   -0.0889971174                      0.071553350
## 497                    0.1792759742                      0.192001685
## 498                    0.1609280040                      0.082854218
## 499                    0.0038429618                      0.081402205
## 500                    0.3062870640                      0.312820562
## 501                   -0.0396154577                      0.135587998
## 502                    0.0944876466                     -0.061637022
## 503                    0.1331526896                      0.031687441
## 504                    0.0358244719                      0.056262001
## 505                    0.3137248632                      0.368258457
## 506                    0.1089464025                      0.072207208
## 507                    0.0317863954                     -0.065388415
## 508                    0.1776382673                      0.032119219
## 509                   -0.2539480779                     -0.066487298
## 510                    0.0915107740                     -0.038631632
## 511                    0.0177776536                     -0.060952798
## 512                    0.3780816806                      0.244289790
## 513                    0.0608177778                     -0.053019547
## 514                    0.5535619104                      0.567812874
## 515                    0.0760235637                     -0.074273674
## 516                   -0.0367337287                     -0.112157092
## 517                    0.6634842208                      0.525829861
## 518                    0.4286444809                      0.356657173
## 519                    0.0038429618                      0.081402205
## 520                    0.0608177778                     -0.053019547
## 521                   -0.0598804475                      0.061749216
## 522                    0.8665406170                      0.457020227
## 523                   -0.0649235274                     -0.047597542
## 524                    0.5860694496                      0.351768436
## 525                   -0.0399287969                     -0.161876473
## 526                    0.2437999279                      0.040565313
## 527                    0.0158976877                     -0.080338591
## 528                    0.0088523099                      0.113491680
## 529                    0.3852679670                      0.204128418
## 530                   -0.1990323019                     -0.088399999
## 531                   -0.1092090426                      0.010954802
## 532                    0.2603510744                      0.151842236
## 533                   -0.1919304470                     -0.141906725
## 534                    0.1466328218                     -0.017096240
## 535                    0.1591809081                      0.065089843
## 536                   -0.0978098580                      0.101744590
## 537                   -0.2416562831                     -0.093893105
## 538                   -0.1553035076                     -0.170782690
## 539                   -0.1061844966                      0.086182360
## 540                    0.0399830448                      0.130872941
## 541                    0.0256270432                     -0.072837826
## 542                   -0.2325863610                     -0.216418074
## 543                    0.0193984191                     -0.060577266
## 544                    0.0218408761                      0.197465957
## 545                   -0.0180715149                     -0.153721005
## 546                    0.1772527482                      0.165155145
## 547                    0.1290457163                      0.044746906
## 548                   -0.0538435701                     -0.052504558
## 549                    0.1786577321                      0.215593138
## 550                    0.2202608504                      0.183511631
## 551                    0.0968439637                     -0.065268100
## 552                    0.1263675172                     -0.032251189
## 553                   -0.0210876242                     -0.047791588
## 554                   -0.0866779595                      0.072677260
## 555                    0.1185160753                     -0.023615763
## 556                    0.3017997519                      0.339132799
## 557                    0.0532085864                     -0.011585188
## 558                   -0.1895827364                     -0.162872664
## 559                   -0.2416562831                     -0.093893105
## 560                    0.0360665822                     -0.253321246
## 561                    0.3259375342                      0.283045399
## 562                   -0.0716334628                      0.160976552
## 563                   -0.0780045461                      0.149341445
## 564                   -0.0978098580                      0.101744590
## 565                   -0.0492801209                     -0.052752012
## 566                    0.1640934111                      0.135360180
## 567                    0.0245503794                      0.080018476
## 568                   -0.0579640970                     -0.264963627
## 569                   -0.1075126712                      0.082366286
## 570                    0.0215402971                      0.139408307
## 571                    0.0811754831                     -0.024374226
## 572                    0.1863740131                      0.160475176
## 573                    0.2703080879                      0.236097089
## 574                   -0.2751233850                     -0.056008588
## 575                   -0.1479682281                     -0.099347729
## 576                    0.2442198325                      0.047893252
## 577                    0.0251849984                     -0.057463913
## 578                   -0.0617014544                     -0.076737748
## 579                   -0.0078891431                      0.050735888
## 580                   -0.0981601210                     -0.128828008
## 581                   -0.1951663535                     -0.064052064
## 582                    0.2440142327                      0.052961861
## 583                    0.0138399478                     -0.014999248
## 584                   -0.0269407965                     -0.001439240
## 585                   -0.1738087149                     -0.067038114
## 586                    0.1855629158                      0.124360806
## 587                    0.1596739225                      0.124049376
## 588                   -0.0516232592                     -0.028314916
## 589                   -0.1284406518                     -0.179607163
## 590                    0.0220773913                      0.205023879
## 591                   -0.2511076050                      0.056772093
## 592                    0.0970517837                     -0.062674224
## 593                    0.1279372228                      0.053936822
## 594                   -0.1546663468                     -0.162248424
## 595                   -0.0579456973                      0.157067751
## 596                   -0.1345712241                     -0.092830773
## 597                    0.1994854236                      0.021568715
## 598                    0.1206160711                      0.029440452
## 599                    0.0270997149                      0.122912734
## 600                   -0.1529699782                     -0.162166975
## 601                    0.2513349730                      0.236085433
## 602                    0.0106947391                      0.058053699
## 603                   -0.0995978027                     -0.073175499
## 604                   -0.0501379941                     -0.053905239
## 605                   -0.0403459700                     -0.114711801
## 606                    0.0957139528                      0.122417238
## 607                    0.2610826284                      0.255123853
## 608                   -0.1003407420                      0.104637023
## 609                    0.0168946159                     -0.016847678
## 610                    0.1262205373                      0.187726505
## 611                    0.0048367237                      0.033070694
## 612                    0.2262673626                      0.228756948
## 613                   -0.0504188859                     -0.218997443
## 614                    0.0106947391                      0.058053699
## 615                    0.1355761562                      0.064627449
## 616                   -0.0233587856                     -0.114118594
## 617                   -0.0735383412                      0.180795263
## 618                    0.1439125461                      0.015206701
## 619                   -0.0673494081                      0.077767917
## 620                   -0.0422622022                      0.149306480
## 621                   -0.0238403813                     -0.116728525
## 622                    0.2109345524                      0.096659364
## 623                    0.0532085864                     -0.011585188
## 624                   -0.0273222073                     -0.112822914
## 625                    0.1253200124                      0.081805285
## 626                   -0.1131153528                     -0.154690031
## 627                    0.0602767432                     -0.039630383
## 628                    0.0016813664                     -0.160708685
## 629                   -0.0567603745                      0.070732355
## 630                    0.0547964672                      0.056046960
## 631                    0.0513435988                     -0.017467038
## 632                   -0.2539480779                     -0.066487298
## 633                    0.0602767432                     -0.039630383
## 634                    0.1139917158                     -0.061310892
## 635                    0.1855629158                      0.124360806
## 636                    0.2262401009                      0.147728404
## 637                    0.1148954593                      0.238039556
## 638                   -0.2420581220                     -0.073681459
## 639                   -0.1601876401                     -0.190171005
## 640                   -0.0616756083                      0.060403795
## 641                   -0.0566048114                      0.065745338
## 642                   -0.0836573733                      0.120665591
## 643                    0.1230805928                      0.080396533
## 644                    0.1828708509                      0.021634297
## 645                   -0.0729754851                     -0.261707554
## 646                   -0.1699473077                     -0.198152528
## 647                    0.1525965715                      0.156600266
## 648                    0.2485577632                      0.261192392
## 649                    0.0469713447                      0.052875383
## 650                   -0.0238403813                     -0.116728525
## 651                    0.1210483974                     -0.025434392
## 652                   -0.2040157266                     -0.193146571
## 653                    0.0218408761                      0.197465957
## 654                    0.1139917158                     -0.061310892
## 655                    0.2343870535                      0.186770147
## 656                    0.2440142327                      0.052961861
## 657                   -0.2408290006                     -0.135464515
## 658                   -0.0403459700                     -0.114711801
## 659                    0.0270210028                      0.081086238
## 660                    0.1789298629                      0.198925579
## 661                   -0.1399117788                     -0.078807709
## 662                   -0.0062141710                     -0.118839471
## 663                    0.0470082543                     -0.054424862
## 664                    0.2474159004                      0.265781109
## 665                    0.0427198583                      0.207439757
## 666                   -0.0233587856                     -0.114118594
## 667                    0.0570109668                     -0.249513057
## 668                    0.0952718385                      0.029291034
## 669                    0.1508768618                      0.150327518
## 670                    0.0477003034                     -0.070698927
## 671                   -0.0273078089                     -0.125485042
## 672                   -0.2920225802                     -0.038636707
## 673                   -0.1998395361                     -0.087279930
## 674                    0.0592930889                     -0.239564717
## 675                    0.0440711599                      0.211922784
## 676                   -0.1911825115                     -0.184536416
## 677                    0.0351986162                      0.063783818
## 678                    0.3321483959                      0.295939222
## 679                   -0.0213541000                     -0.037635908
## 680                   -0.0283810341                      0.045730028
## 681                   -0.0278029006                      0.116375504
## 682                    0.0991999354                     -0.077260020
## 683                   -0.1479682281                     -0.099347729
## 684                   -0.1529699782                     -0.162166975
## 685                   -0.1801157298                     -0.058386497
## 686                    0.5892681493                      0.362421235
## 687                    0.1153603975                     -0.044382530
## 688                   -0.2036741609                     -0.039769197
## 689                   -0.2310273289                      0.073559580
## 690                   -0.2397809140                     -0.099316812
## 691                    0.0177776536                     -0.060952798
## 692                    0.0757411365                     -0.305000403
## 693                   -0.2404518511                     -0.056957703
## 694                    0.1280480326                      0.082233278
## 695                    0.0011017971                     -0.167447661
## 696                    0.1828708509                      0.021634297
## 697                   -0.2488409473                     -0.127770258
## 698                   -0.0538435701                     -0.052504558
## 699                   -0.0817365488                      0.033406215
## 700                    0.2457466612                      0.237382595
## 701                    0.0343416332                      0.125124701
## 702                    0.0036188681                     -0.067674332
## 703                   -0.0569788499                      0.156491208
## 704                   -0.0291597296                     -0.115646114
## 705                   -0.0634511986                     -0.021639009
## 706                   -0.0176903110                     -0.084917297
## 707                   -0.0275778847                     -0.123715119
## 708                    0.0602767432                     -0.039630383
## 709                    0.2215189103                      0.230934812
## 710                   -0.0275482108                     -0.095349021
## 711                    0.0259808749                     -0.103151898
## 712                    0.2610826284                      0.255123853
## 713                   -0.2234810591                     -0.148551281
## 714                   -0.2019785736                     -0.191306912
## 715                   -0.1700361501                     -0.039666847
## 716                    0.0215402971                      0.139408307
## 717                    0.0369586317                      0.129606546
## 718                   -0.0669573719                      0.134617852
## 719                    0.0608152785                     -0.065491757
## 720                   -0.0422622022                      0.149306480
## 721                   -0.0263842940                      0.024749049
## 722                    0.0312537810                      0.201324546
## 723                    0.3149651302                      0.280959188
## 724                    0.0949270706                      0.039314863
## 725                   -0.0683671837                     -0.053118315
## 726                   -0.0062141710                     -0.118839471
## 727                   -0.2327569063                      0.099865443
## 728                    0.3381208068                      0.223734614
## 729                   -0.0534830317                     -0.221093664
## 730                    0.4075669663                      0.362039312
## 731                    0.1341173865                      0.119032116
## 732                    0.1936250264                      0.156580032
## 733                    0.1480988146                      0.136820269
## 734                   -0.1769853115                     -0.060061547
## 735                    0.3729517890                      0.232347378
## 736                    0.1013126458                     -0.079562195
## 737                   -0.1081122171                      0.125232770
## 738                   -0.0401654688                      0.245991929
## 739                   -0.0252046727                     -0.098649765
## 740                    0.2474463685                      0.058585656
## 741                   -0.1652165634                     -0.187663092
## 742                    0.0043561268                     -0.059746715
## 743                    0.0608177778                     -0.053019547
## 744                   -0.0422039527                      0.022523596
## 745                    0.1780667325                      0.176014393
## 746                    0.0051825517                      0.134244829
## 747                    0.1016160680                      0.141705779
## 748                    0.1016160680                      0.141705779
## 749                    0.0931738771                     -0.064056742
## 750                   -0.1081122171                      0.125232770
## 751                   -0.1526752457                     -0.288304758
## 752                    0.1253200124                      0.081805285
## 753                    0.3729517890                      0.232347378
## 754                   -0.0058976807                     -0.116435690
## 755                   -0.0428683961                      0.172914501
## 756                    0.2457466612                      0.237382595
## 757                    0.0040419068                     -0.056321510
## 758                    0.3377366262                      0.227145066
## 759                    0.0288125833                     -0.078169054
## 760                   -0.0387478305                      0.049864166
## 761                    0.0088523099                      0.113491680
## 762                   -0.2087056220                     -0.080828676
## 763                    0.2442198325                      0.047893252
## 764                   -0.1017580329                     -0.080268924
## 765                    0.1139917158                     -0.061310892
## 766                   -0.2481048554                     -0.118897889
## 767                    0.2272530986                      0.184312705
## 768                    0.0957139528                      0.122417238
## 769                    0.0570109668                     -0.249513057
## 770                   -0.1357275097                     -0.080527159
## 771                   -0.1251437754                     -0.179884725
## 772                    0.0600911366                      0.068266382
## 773                   -0.1452043967                     -0.118065128
## 774                    0.0592930889                     -0.239564717
## 775                    0.2227473230                      0.141677756
## 776                    0.0936942466                      0.120191319
## 777                    0.1279372228                      0.053936822
## 778                    0.1518914203                      0.175957065
## 779                    0.0501582127                     -0.245644087
## 780                    0.1525965715                      0.156600266
## 781                   -0.1526670151                     -0.046753048
## 782                   -0.1601876401                     -0.190171005
## 783                    0.1486286779                      0.131823223
## 784                    0.1490174357                      0.164873601
## 785                    0.0369586317                      0.129606546
## 786                   -0.0649235274                     -0.047597542
## 787                    0.0687768538                     -0.062447167
## 788                    0.1343654765                      0.116747226
## 789                    0.4843476105                      0.537389131
## 790                    0.1048743980                      0.088023739
## 791                   -0.1895827364                     -0.162872664
## 792                   -0.2407844420                     -0.089322073
## 793                    0.0650586765                     -0.045734843
## 794                    0.1789859482                      0.191509957
## 795                    0.0759994140                     -0.069675751
## 796                   -0.1896137684                     -0.198248375
## 797                    0.1781801573                      0.188524083
## 798                    0.3398501608                      0.241001238
## 799                    0.0608152785                     -0.065491757
## 800                    0.1486194798                      0.157704279
## 801                    0.1828708509                      0.021634297
## 802                   -0.0516232592                     -0.028314916
## 803                   -0.2604384295                     -0.073338560
## 804                    0.1808454468                      0.191701222
## 805                   -0.0112333154                     -0.105749754
## 806                    0.0284313223                     -0.078681167
## 807                    0.3201531772                      0.135649661
## 808                    0.0496033370                     -0.291900358
## 809                   -0.2273063640                      0.072353060
## 810                   -0.0365237090                     -0.100909954
## 811                    0.1284219695                     -0.072268254
## 812                    0.1431210048                      0.097248493
## 813                    0.0055565930                     -0.065750229
##     posterior_mean_hard_skill_loser posterior_sd_clay_skill_loser
## 1                       0.619732577                    0.05639436
## 2                       0.552658531                    0.05491178
## 3                       0.696610108                    0.04479313
## 4                       0.096195744                    0.08810323
## 5                       0.298606420                    0.04302091
## 6                       0.020522313                    0.06298781
## 7                       0.650440124                    0.05632306
## 8                       0.190631420                    0.06564664
## 9                       0.034099630                    0.08905587
## 10                      0.572148401                    0.05338247
## 11                      0.568007636                    0.05102113
## 12                      0.302910763                    0.04152946
## 13                      0.200454597                    0.08179548
## 14                      0.553268335                    0.05507212
## 15                      0.217885815                    0.04973562
## 16                      0.591180899                    0.05638412
## 17                      0.564121349                    0.04615653
## 18                      0.408437547                    0.04061636
## 19                      0.670357282                    0.05006213
## 20                      0.114395862                    0.07850898
## 21                      0.129987128                    0.07792433
## 22                      0.338051598                    0.05111582
## 23                      0.285767569                    0.07075347
## 24                      0.161116472                    0.05109091
## 25                      0.211806088                    0.04620997
## 26                     -0.053339360                    0.11038046
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## 491                     0.364728613                    0.05263435
## 492                     0.105707689                    0.07611988
## 493                     0.004115687                    0.05724258
## 494                    -0.091690746                    0.11111850
## 495                    -0.072934579                    0.13489247
## 496                     0.047450714                    0.05727799
## 497                     0.214068766                    0.04611321
## 498                     0.083877606                    0.04388024
## 499                     0.086173740                    0.12980010
## 500                     0.339020581                    0.04476291
## 501                     0.068956655                    0.08219929
## 502                    -0.032214539                    0.05417951
## 503                     0.052317387                    0.08310220
## 504                     0.051310463                    0.15770306
## 505                     0.356701793                    0.05995268
## 506                     0.073150017                    0.05197914
## 507                    -0.059254130                    0.10886824
## 508                     0.049329115                    0.04301127
## 509                    -0.087986936                    0.10740224
## 510                    -0.058395190                    0.06393812
## 511                    -0.078276382                    0.05786220
## 512                     0.310426217                    0.03976896
## 513                    -0.067979741                    0.06012102
## 514                     0.629338801                    0.04577598
## 515                    -0.042782516                    0.05213129
## 516                    -0.130041788                    0.07044118
## 517                     0.651647291                    0.04883553
## 518                     0.377703155                    0.04899048
## 519                     0.086173740                    0.12980010
## 520                    -0.067979741                    0.06012102
## 521                     0.058235733                    0.09017086
## 522                     0.563637965                    0.05529928
## 523                    -0.042432506                    0.14142666
## 524                     0.419056452                    0.04160549
## 525                    -0.113122290                    0.06825028
## 526                     0.124791184                    0.05155727
## 527                    -0.089556926                    0.05848916
## 528                     0.096195744                    0.08810323
## 529                     0.333678022                    0.04498681
## 530                    -0.134119744                    0.10538521
## 531                    -0.006247142                    0.10024733
## 532                     0.190631420                    0.06564664
## 533                    -0.181203858                    0.10235982
## 534                     0.009115973                    0.06200015
## 535                     0.052574954                    0.04737776
## 536                     0.006998193                    0.09884677
## 537                    -0.149199774                    0.09479025
## 538                    -0.190384849                    0.10582200
## 539                     0.057314438                    0.06555290
## 540                     0.145399151                    0.05812900
## 541                    -0.099363700                    0.04427820
## 542                    -0.247921611                    0.14821109
## 543                    -0.076262262                    0.05768097
## 544                     0.152212623                    0.06538713
## 545                    -0.143368781                    0.10105023
## 546                     0.173293300                    0.04918036
## 547                     0.043713269                    0.06962695
## 548                    -0.039316825                    0.06641383
## 549                     0.223831431                    0.04485072
## 550                     0.242032308                    0.04140860
## 551                    -0.035749648                    0.05392494
## 552                     0.003456174                    0.05911229
## 553                    -0.029793397                    0.06386525
## 554                     0.046361071                    0.05652346
## 555                     0.008513392                    0.05441775
## 556                     0.355449652                    0.06421297
## 557                    -0.041584221                    0.07069865
## 558                    -0.188329315                    0.14378183
## 559                    -0.149199774                    0.09479025
## 560                    -0.189042758                    0.05065140
## 561                     0.306634122                    0.04786831
## 562                     0.095486838                    0.06783261
## 563                     0.062980068                    0.06649829
## 564                     0.006998193                    0.09884677
## 565                    -0.035370009                    0.06626277
## 566                     0.162152091                    0.05305703
## 567                     0.038180813                    0.06063541
## 568                    -0.240306470                    0.06862293
## 569                     0.057228478                    0.06477707
## 570                     0.095013567                    0.04696526
## 571                     0.000249626                    0.04573788
## 572                     0.202361983                    0.05435362
## 573                     0.291312327                    0.05961764
## 574                    -0.097302305                    0.10943645
## 575                    -0.118921419                    0.12076266
## 576                     0.134288764                    0.05116932
## 577                    -0.056210267                    0.09511151
## 578                    -0.068434478                    0.12613507
## 579                     0.045977750                    0.09560185
## 580                    -0.123526587                    0.08913276
## 581                    -0.132483532                    0.14789823
## 582                     0.142857426                    0.05383115
## 583                    -0.030140463                    0.06663000
## 584                    -0.003884790                    0.08780896
## 585                    -0.097937961                    0.09445337
## 586                     0.136475161                    0.06287991
## 587                     0.179410243                    0.05097449
## 588                    -0.019361873                    0.13792932
## 589                    -0.190275863                    0.09182076
## 590                     0.158016110                    0.06554770
## 591                    -0.009999782                    0.10221383
## 592                    -0.031234047                    0.05457817
## 593                     0.083635071                    0.10510809
## 594                    -0.179351399                    0.08369012
## 595                     0.086480194                    0.05942073
## 596                    -0.091799886                    0.07103334
## 597                     0.099378598                    0.06881421
## 598                     0.052155734                    0.05649631
## 599                     0.088919370                    0.04693497
## 600                    -0.182809501                    0.08412035
## 601                     0.298746430                    0.05774596
## 602                     0.067428516                    0.10223930
## 603                    -0.097837334                    0.08520918
## 604                    -0.040574518                    0.06725118
## 605                    -0.127592102                    0.06809022
## 606                     0.105707689                    0.07611988
## 607                     0.289965810                    0.07051161
## 608                     0.010919039                    0.09797638
## 609                    -0.029652116                    0.06618594
## 610                     0.130391488                    0.05043014
## 611                     0.019500565                    0.15634319
## 612                     0.213634357                    0.04688154
## 613                    -0.195536846                    0.06266460
## 614                     0.067428516                    0.10223930
## 615                     0.095626615                    0.09492671
## 616                    -0.139089542                    0.06878132
## 617                     0.104851500                    0.06933176
## 618                     0.014512366                    0.04974128
## 619                     0.031737976                    0.14294287
## 620                     0.071474986                    0.06281565
## 621                    -0.137450327                    0.06844496
## 622                     0.131968032                    0.07556243
## 623                    -0.041584221                    0.07069865
## 624                    -0.138084985                    0.06841489
## 625                     0.095580459                    0.04414434
## 626                    -0.160435689                    0.08964147
## 627                    -0.019130273                    0.11820843
## 628                    -0.150377128                    0.04715480
## 629                     0.051424635                    0.08997125
## 630                     0.087681655                    0.08830055
## 631                    -0.050801401                    0.07187276
## 632                    -0.087986936                    0.10740224
## 633                    -0.019130273                    0.11820843
## 634                    -0.060180459                    0.03913300
## 635                     0.136475161                    0.06287991
## 636                     0.167270978                    0.07450633
## 637                     0.219972145                    0.05740322
## 638                    -0.096977681                    0.09995546
## 639                    -0.207608668                    0.10182861
## 640                     0.058157452                    0.09466805
## 641                     0.058473783                    0.09313736
## 642                     0.016925126                    0.10298129
## 643                     0.082389434                    0.05306544
## 644                     0.092275244                    0.06421783
## 645                    -0.241550991                    0.06151165
## 646                    -0.223414363                    0.08508126
## 647                     0.134635498                    0.05451085
## 648                     0.294260472                    0.07130687
## 649                     0.059845362                    0.19884605
## 650                    -0.137450327                    0.06844496
## 651                     0.011750047                    0.05482882
## 652                    -0.203837352                    0.10436723
## 653                     0.152212623                    0.06538713
## 654                    -0.060180459                    0.03913300
## 655                     0.212311370                    0.04958789
## 656                     0.142857426                    0.05383115
## 657                    -0.174691510                    0.11479641
## 658                    -0.127592102                    0.06809022
## 659                     0.112957312                    0.06722232
## 660                     0.234344429                    0.05176518
## 661                    -0.112830936                    0.09936153
## 662                    -0.099034315                    0.06979231
## 663                    -0.042161817                    0.07544841
## 664                     0.287774337                    0.07002051
## 665                     0.167259252                    0.06777900
## 666                    -0.139089542                    0.06878132
## 667                    -0.171459491                    0.05190624
## 668                     0.041515967                    0.06404474
## 669                     0.135957318                    0.05438628
## 670                    -0.079340990                    0.04146952
## 671                    -0.136818431                    0.06989761
## 672                    -0.060731222                    0.11339908
## 673                    -0.134641579                    0.09895838
## 674                    -0.165936664                    0.04885030
## 675                     0.169003207                    0.06553069
## 676                    -0.206582096                    0.11327488
## 677                     0.109692501                    0.06106280
## 678                     0.310820545                    0.04734909
## 679                    -0.028627398                    0.12485749
## 680                     0.029744822                    0.06866240
## 681                     0.090164746                    0.09847540
## 682                    -0.032673020                    0.05373705
## 683                    -0.118921419                    0.12076266
## 684                    -0.182809501                    0.08412035
## 685                    -0.093968106                    0.09825819
## 686                     0.438027578                    0.03991229
## 687                    -0.057404905                    0.06613040
## 688                    -0.126195297                    0.14036267
## 689                     0.011744717                    0.08274683
## 690                    -0.152040166                    0.09880287
## 691                    -0.078276382                    0.05786220
## 692                    -0.195765865                    0.04442255
## 693                    -0.082880154                    0.10398002
## 694                     0.082911783                    0.05461256
## 695                    -0.151832759                    0.04781210
## 696                     0.092275244                    0.06421783
## 697                    -0.196088504                    0.09113809
## 698                    -0.039316825                    0.06641383
## 699                     0.023479262                    0.07789774
## 700                     0.298688230                    0.05866213
## 701                     0.141284107                    0.05863912
## 702                    -0.089809526                    0.06024487
## 703                     0.096250848                    0.07947042
## 704                    -0.135536822                    0.06671775
## 705                    -0.017911275                    0.11609518
## 706                    -0.081945830                    0.09754458
## 707                    -0.138431748                    0.06695635
## 708                    -0.019130273                    0.11820843
## 709                     0.275780163                    0.05625224
## 710                    -0.098053118                    0.06631875
## 711                    -0.090281481                    0.10385718
## 712                     0.289965810                    0.07051161
## 713                    -0.196098254                    0.10185008
## 714                    -0.202283107                    0.10578575
## 715                    -0.073966449                    0.12143283
## 716                     0.095013567                    0.04696526
## 717                     0.147839060                    0.05806294
## 718                     0.062251875                    0.07723036
## 719                    -0.081233250                    0.06258633
## 720                     0.071474986                    0.06281565
## 721                     0.038861895                    0.06553893
## 722                     0.162111628                    0.06693238
## 723                     0.331037440                    0.04642929
## 724                     0.049952584                    0.05361226
## 725                    -0.058859648                    0.14194608
## 726                    -0.099034315                    0.06979231
## 727                     0.015217503                    0.08482663
## 728                     0.280636740                    0.04426879
## 729                    -0.201029228                    0.06074436
## 730                     0.390646244                    0.04780014
## 731                     0.136871140                    0.06168182
## 732                     0.189265763                    0.05554731
## 733                     0.185310722                    0.06665784
## 734                    -0.096005804                    0.09268015
## 735                     0.301143691                    0.03919288
## 736                    -0.026960193                    0.09588256
## 737                     0.019338904                    0.10215245
## 738                     0.142319341                    0.08203376
## 739                    -0.075967130                    0.13938501
## 740                     0.142973033                    0.05220436
## 741                    -0.211595242                    0.08172319
## 742                    -0.084783593                    0.06282690
## 743                    -0.067979741                    0.06012102
## 744                     0.029050311                    0.06447349
## 745                     0.224162248                    0.05229728
## 746                     0.107189440                    0.09150053
## 747                     0.130742498                    0.07700020
## 748                     0.130742498                    0.07700020
## 749                    -0.031259345                    0.05342015
## 750                     0.019338904                    0.10215245
## 751                    -0.304502230                    0.06524955
## 752                     0.095580459                    0.04414434
## 753                     0.301143691                    0.03919288
## 754                    -0.094910496                    0.07107057
## 755                     0.075674096                    0.08259089
## 756                     0.298688230                    0.05866213
## 757                    -0.079389146                    0.06152925
## 758                     0.286704022                    0.04416272
## 759                    -0.098411087                    0.04109732
## 760                     0.036713414                    0.10948237
## 761                     0.096195744                    0.08810323
## 762                    -0.138096448                    0.10257440
## 763                     0.134288764                    0.05116932
## 764                    -0.106329777                    0.08266755
## 765                    -0.060180459                    0.03913300
## 766                    -0.175517279                    0.12089885
## 767                     0.251933542                    0.04722426
## 768                     0.105707689                    0.07611988
## 769                    -0.171459491                    0.05190624
## 770                    -0.091855591                    0.07341467
## 771                    -0.187800745                    0.09244820
## 772                     0.097855934                    0.08670309
## 773                    -0.137195337                    0.11061740
## 774                    -0.165936664                    0.04885030
## 775                     0.163306930                    0.07684625
## 776                     0.107076354                    0.07739058
## 777                     0.083635071                    0.10510809
## 778                     0.224261672                    0.06278897
## 779                    -0.184500966                    0.05104849
## 780                     0.134635498                    0.05451085
## 781                    -0.077264389                    0.10671378
## 782                    -0.207608668                    0.10182861
## 783                     0.136071269                    0.07318378
## 784                     0.128978898                    0.06285815
## 785                     0.147839060                    0.05806294
## 786                    -0.042432506                    0.14142666
## 787                    -0.070868326                    0.03910497
## 788                     0.134628842                    0.05945485
## 789                     0.576554488                    0.05510547
## 790                     0.110647187                    0.18651600
## 791                    -0.188329315                    0.14378183
## 792                    -0.142457961                    0.09903085
## 793                    -0.053415892                    0.06066155
## 794                     0.218259288                    0.05080290
## 795                    -0.037892570                    0.05100977
## 796                    -0.219776784                    0.10225944
## 797                     0.211949358                    0.04901914
## 798                     0.313743243                    0.04177429
## 799                    -0.081233250                    0.06258633
## 800                     0.132217607                    0.06287007
## 801                     0.092275244                    0.06421783
## 802                    -0.019361873                    0.13792932
## 803                    -0.095212883                    0.10813651
## 804                     0.215937957                    0.05155898
## 805                    -0.130389534                    0.06619922
## 806                    -0.102125270                    0.04034265
## 807                     0.194419553                    0.03965439
## 808                    -0.210626406                    0.05771370
## 809                     0.003461002                    0.08347318
## 810                    -0.097752174                    0.09677711
## 811                    -0.056344180                    0.05665397
## 812                     0.085393161                    0.04158810
## 813                    -0.065411055                    0.08655141
##     posterior_sd_grass_skill_loser posterior_sd_hard_skill_loser
## 1                       0.06483414                    0.03874547
## 2                       0.07262470                    0.03808659
## 3                       0.05112788                    0.02877483
## 4                       0.08102545                    0.05893546
## 5                       0.06036466                    0.03501735
## 6                       0.06997370                    0.04884237
## 7                       0.05592768                    0.03467593
## 8                       0.05749036                    0.03947404
## 9                       0.11370242                    0.08476657
## 10                      0.05104362                    0.03311984
## 11                      0.07155328                    0.03444101
## 12                      0.05267278                    0.02781009
## 13                      0.08589515                    0.06428037
## 14                      0.06923868                    0.03668121
## 15                      0.05452255                    0.03622598
## 16                      0.05013394                    0.03266847
## 17                      0.05881047                    0.03367400
## 18                      0.05377108                    0.03488120
## 19                      0.05225887                    0.03251625
## 20                      0.06568090                    0.04760436
## 21                      0.07964736                    0.04900843
## 22                      0.05765051                    0.03531909
## 23                      0.06647786                    0.04189059
## 24                      0.05712610                    0.03765395
## 25                      0.05346641                    0.02931303
## 26                      0.09644487                    0.07680743
## 27                      0.08468002                    0.05775564
## 28                      0.07109896                    0.03523428
## 29                      0.05452255                    0.03622598
## 30                      0.05738338                    0.03561002
## 31                      0.05425036                    0.03336004
## 32                      0.05217510                    0.03313153
## 33                      0.05616623                    0.03185768
## 34                      0.05972948                    0.03339870
## 35                      0.05945591                    0.04088127
## 36                      0.06791495                    0.03994066
## 37                      0.06441698                    0.04104843
## 38                      0.05744166                    0.04110085
## 39                      0.07631672                    0.05237974
## 40                      0.07421337                    0.04319859
## 41                      0.07111446                    0.04067891
## 42                      0.06199250                    0.04029778
## 43                      0.05631806                    0.03596678
## 44                      0.06435020                    0.03422801
## 45                      0.05258992                    0.03288167
## 46                      0.04867487                    0.03101102
## 47                      0.06106690                    0.03278546
## 48                      0.06732510                    0.03946948
## 49                      0.06627109                    0.03362362
## 50                      0.07207901                    0.03640019
## 51                      0.06868180                    0.03852030
## 52                      0.05589817                    0.03769608
## 53                      0.04928490                    0.03294182
## 54                      0.05686890                    0.04294763
## 55                      0.07799150                    0.05913392
## 56                      0.06078001                    0.03376147
## 57                      0.05755088                    0.03506741
## 58                      0.05858933                    0.03285602
## 59                      0.06572853                    0.04649704
## 60                      0.06216823                    0.04118072
## 61                      0.05613757                    0.03169713
## 62                      0.06159037                    0.03618107
## 63                      0.05238698                    0.02869089
## 64                      0.06605952                    0.05344841
## 65                      0.06019138                    0.03310314
## 66                      0.05940144                    0.03374546
## 67                      0.05686810                    0.03143779
## 68                      0.06461213                    0.04734733
## 69                      0.10851805                    0.08506144
## 70                      0.07029298                    0.03590528
## 71                      0.07272612                    0.04211542
## 72                      0.06814180                    0.04469878
## 73                      0.05674429                    0.03482726
## 74                      0.06399081                    0.03713871
## 75                      0.05608604                    0.03469927
## 76                      0.06316559                    0.04490549
## 77                      0.05519188                    0.03462184
## 78                      0.09213504                    0.08286882
## 79                      0.05158986                    0.03241119
## 80                      0.06410157                    0.03708863
## 81                      0.05711879                    0.03506771
## 82                      0.05603962                    0.04061396
## 83                      0.06568090                    0.04760436
## 84                      0.09515545                    0.07873630
## 85                      0.05783549                    0.03562709
## 86                      0.06065237                    0.03147918
## 87                      0.05380926                    0.02861961
## 88                      0.06324049                    0.03695188
## 89                      0.06309889                    0.04879669
## 90                      0.07589978                    0.04989117
## 91                      0.08075903                    0.05166083
## 92                      0.05349159                    0.03676116
## 93                      0.04738877                    0.02878024
## 94                      0.05581219                    0.03016277
## 95                      0.05021059                    0.02991752
## 96                      0.04849251                    0.02999538
## 97                      0.07156333                    0.05500410
## 98                      0.08684534                    0.05071583
## 99                      0.05803739                    0.02927431
## 100                     0.06109613                    0.04059468
## 101                     0.05807346                    0.03916857
## 102                     0.06520045                    0.03803596
## 103                     0.05475480                    0.03224731
## 104                     0.05660060                    0.03168982
## 105                     0.07557854                    0.04498351
## 106                     0.05345756                    0.03352282
## 107                     0.05976368                    0.03435995
## 108                     0.07548740                    0.04565927
## 109                     0.07703504                    0.04553052
## 110                     0.08945258                    0.06536024
## 111                     0.06288638                    0.03960851
## 112                     0.06882187                    0.04843606
## 113                     0.06856413                    0.04703352
## 114                     0.05194220                    0.03188999
## 115                     0.06783249                    0.04015282
## 116                     0.05457030                    0.04003953
## 117                     0.06277423                    0.04399318
## 118                     0.06854700                    0.03869567
## 119                     0.05250631                    0.03206428
## 120                     0.06106079                    0.03766935
## 121                     0.08152092                    0.04202311
## 122                     0.07006215                    0.03997282
## 123                     0.06052761                    0.03835352
## 124                     0.05217510                    0.03313153
## 125                     0.06370334                    0.03773953
## 126                     0.08777995                    0.07257855
## 127                     0.05945591                    0.04088127
## 128                     0.05473950                    0.03312023
## 129                     0.09644487                    0.07680743
## 130                     0.05208125                    0.03209939
## 131                     0.07634539                    0.05839977
## 132                     0.06412014                    0.04642580
## 133                     0.08056839                    0.07355168
## 134                     0.05709970                    0.03230226
## 135                     0.08007651                    0.04841098
## 136                     0.06089091                    0.03516712
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## 620                     0.06692585                    0.03989427
## 621                     0.07182660                    0.04965371
## 622                     0.06971604                    0.04693281
## 623                     0.07910770                    0.06348928
## 624                     0.07303110                    0.05047751
## 625                     0.05723496                    0.03773771
## 626                     0.11572311                    0.08997952
## 627                     0.08753697                    0.06687796
## 628                     0.08056287                    0.05354138
## 629                     0.06416028                    0.05152797
## 630                     0.08793084                    0.07169546
## 631                     0.07793098                    0.06221472
## 632                     0.06927541                    0.05053540
## 633                     0.08753697                    0.06687796
## 634                     0.05973710                    0.04262823
## 635                     0.05701689                    0.04151413
## 636                     0.06238891                    0.04269066
## 637                     0.04907446                    0.03155764
## 638                     0.07299206                    0.04798655
## 639                     0.12516294                    0.10748716
## 640                     0.06370561                    0.04467488
## 641                     0.06218698                    0.04430455
## 642                     0.06941670                    0.04672314
## 643                     0.06895388                    0.04336378
## 644                     0.07731954                    0.04131676
## 645                     0.12079421                    0.09816466
## 646                     0.09224631                    0.08144263
## 647                     0.05418796                    0.03543144
## 648                     0.06814180                    0.04469878
## 649                     0.17390845                    0.17565352
## 650                     0.07182660                    0.04965371
## 651                     0.07010466                    0.04681984
## 652                     0.13070959                    0.11486474
## 653                     0.05880137                    0.03712406
## 654                     0.05973710                    0.04262823
## 655                     0.06159037                    0.03618107
## 656                     0.07557854                    0.04498351
## 657                     0.09346879                    0.07960615
## 658                     0.07589978                    0.04989117
## 659                     0.06294350                    0.04057094
## 660                     0.05616623                    0.03185768
## 661                     0.08929171                    0.07929121
## 662                     0.08958166                    0.06756876
## 663                     0.07375659                    0.05114495
## 664                     0.07373740                    0.04814434
## 665                     0.06418663                    0.03744168
## 666                     0.07234540                    0.05140835
## 667                     0.08591171                    0.05436784
## 668                     0.07506181                    0.04993507
## 669                     0.05366674                    0.03706885
## 670                     0.06316559                    0.04490549
## 671                     0.07248877                    0.05101835
## 672                     0.07948485                    0.05308449
## 673                     0.07769129                    0.06016798
## 674                     0.08337907                    0.05671274
## 675                     0.06370233                    0.03908059
## 676                     0.12843703                    0.11642613
## 677                     0.06292173                    0.03723323
## 678                     0.05967715                    0.03387687
## 679                     0.08953207                    0.07116069
## 680                     0.06655516                    0.05169624
## 681                     0.07887332                    0.05919885
## 682                     0.08991664                    0.06329749
## 683                     0.14104657                    0.12784749
## 684                     0.08488069                    0.07082314
## 685                     0.07902358                    0.05661653
## 686                     0.05382854                    0.03156357
## 687                     0.07963156                    0.05618883
## 688                     0.06571459                    0.05430301
## 689                     0.06000543                    0.04297320
## 690                     0.07634539                    0.05839977
## 691                     0.07699145                    0.05691942
## 692                     0.08179756                    0.05347555
## 693                     0.07113053                    0.04763499
## 694                     0.06778821                    0.04525831
## 695                     0.07863033                    0.05094850
## 696                     0.07731954                    0.04131676
## 697                     0.10128856                    0.07770006
## 698                     0.07083049                    0.04918478
## 699                     0.06562334                    0.04685533
## 700                     0.06338538                    0.03464497
## 701                     0.05346797                    0.03922608
## 702                     0.07329403                    0.05731750
## 703                     0.06456722                    0.04421753
## 704                     0.07111162                    0.05008626
## 705                     0.07779966                    0.06379707
## 706                     0.08331952                    0.06632276
## 707                     0.07431178                    0.04915187
## 708                     0.08753697                    0.06687796
## 709                     0.05972948                    0.03339870
## 710                     0.09176889                    0.06108545
## 711                     0.11095967                    0.10372218
## 712                     0.06760015                    0.04167647
## 713                     0.08395840                    0.06650350
## 714                     0.13390225                    0.11420945
## 715                     0.08184599                    0.05614144
## 716                     0.07547847                    0.04821869
## 717                     0.05218262                    0.03664799
## 718                     0.06856413                    0.04703352
## 719                     0.07395500                    0.05077570
## 720                     0.06692585                    0.03989427
## 721                     0.07531209                    0.05007817
## 722                     0.06161500                    0.03703039
## 723                     0.05208125                    0.03209939
## 724                     0.06728641                    0.04786895
## 725                     0.08268485                    0.05702308
## 726                     0.08958166                    0.06756876
## 727                     0.06718914                    0.04476486
## 728                     0.06290700                    0.04003230
## 729                     0.09918625                    0.08308742
## 730                     0.05289130                    0.03025847
## 731                     0.07564028                    0.04460858
## 732                     0.05616218                    0.03367843
## 733                     0.06324049                    0.03695188
## 734                     0.07266016                    0.05381379
## 735                     0.05836956                    0.03448727
## 736                     0.10430103                    0.07119358
## 737                     0.07296621                    0.04460748
## 738                     0.07321858                    0.04093846
## 739                     0.08650905                    0.07640071
## 740                     0.07040859                    0.04515370
## 741                     0.08688716                    0.07498656
## 742                     0.07650982                    0.05573459
## 743                     0.07746883                    0.05501883
## 744                     0.07530801                    0.04779189
## 745                     0.06442653                    0.03424683
## 746                     0.06848699                    0.05249895
## 747                     0.06553642                    0.04774870
## 748                     0.06553642                    0.04774870
## 749                     0.08456680                    0.06248878
## 750                     0.07296621                    0.04460748
## 751                     0.09083264                    0.07803320
## 752                     0.05723496                    0.03773771
## 753                     0.05836956                    0.03448727
## 754                     0.09134435                    0.06358732
## 755                     0.07866778                    0.05283007
## 756                     0.06338538                    0.03464497
## 757                     0.07531578                    0.05834423
## 758                     0.06322161                    0.03624544
## 759                     0.06290009                    0.04496225
## 760                     0.07375296                    0.05618030
## 761                     0.08102545                    0.05893546
## 762                     0.08649623                    0.05907793
## 763                     0.07548740                    0.04565927
## 764                     0.07853787                    0.07188147
## 765                     0.05973710                    0.04262823
## 766                     0.10374020                    0.08441909
## 767                     0.05879797                    0.03368153
## 768                     0.06309889                    0.04879669
## 769                     0.08591171                    0.05436784
## 770                     0.06812085                    0.04849561
## 771                     0.12075576                    0.10114142
## 772                     0.08894492                    0.07985487
## 773                     0.13500874                    0.12096509
## 774                     0.08337907                    0.05671274
## 775                     0.06464061                    0.04320236
## 776                     0.06810159                    0.05347424
## 777                     0.08689701                    0.07517294
## 778                     0.07278791                    0.03457902
## 779                     0.08945258                    0.06536024
## 780                     0.05418796                    0.03543144
## 781                     0.07473122                    0.05941034
## 782                     0.12516294                    0.10748716
## 783                     0.06285411                    0.04664417
## 784                     0.06840863                    0.03931538
## 785                     0.05218262                    0.03664799
## 786                     0.08358357                    0.07186021
## 787                     0.05947745                    0.04450771
## 788                     0.07113039                    0.04434575
## 789                     0.05999314                    0.03570408
## 790                     0.13391047                    0.14278260
## 791                     0.11159153                    0.09991319
## 792                     0.08532442                    0.06107349
## 793                     0.07284978                    0.04936798
## 794                     0.05513372                    0.03018383
## 795                     0.08623510                    0.05924004
## 796                     0.12577487                    0.10883146
## 797                     0.05102035                    0.03037361
## 798                     0.05429955                    0.03419707
## 799                     0.07395500                    0.05077570
## 800                     0.06482760                    0.03868171
## 801                     0.07731954                    0.04131676
## 802                     0.09213504                    0.08286882
## 803                     0.07145610                    0.04986815
## 804                     0.05581219                    0.03016277
## 805                     0.07235735                    0.05115666
## 806                     0.06368971                    0.04478053
## 807                     0.06711270                    0.04028321
## 808                     0.09960867                    0.07113439
## 809                     0.06412673                    0.04071659
## 810                     0.10971127                    0.08089051
## 811                     0.07729352                    0.06151708
## 812                     0.04906827                    0.03494947
## 813                     0.08668479                    0.07479225
##     posterior_median_clay_skill_loser posterior_median_grass_skill_loser
## 1                         0.581937900                        0.534864950
## 2                         0.839696500                        0.462714500
## 3                         0.683472750                        0.595666000
## 4                         0.008674050                        0.112087150
## 5                         0.335594450                        0.236945450
## 6                        -0.045853750                        0.016698145
## 7                         0.657310950                        0.518615000
## 8                         0.258008700                        0.150060700
## 9                         0.095319800                        0.012080000
## 10                        0.482158350                        0.524291450
## 11                        0.876961500                        0.442632800
## 12                        0.355995600                        0.282640240
## 13                        0.159870400                        0.180367700
## 14                        0.859280000                        0.448338350
## 15                        0.230948670                        0.213835659
## 16                        0.486621300                        0.558303120
## 17                        0.893748000                        0.457424500
## 18                        0.584271500                        0.333582550
## 19                        0.660960350                        0.561930000
## 20                        0.096365700                        0.127942600
## 21                        0.214379400                        0.075039350
## 22                        0.299887310                        0.285205400
## 23                        0.254525450                        0.250172200
## 24                        0.146855400                        0.142314400
## 25                        0.178494550                        0.192145625
## 26                       -0.025335725                       -0.050877350
## 27                        0.013231650                       -0.124881680
## 28                        0.863796500                        0.444544000
## 29                        0.230948670                        0.213835659
## 30                        0.269853750                        0.237010950
## 31                        0.191090150                        0.157252100
## 32                        0.142490935                        0.112436450
## 33                        0.178792550                        0.197835450
## 34                        0.219871350                        0.231582700
## 35                        0.228242450                        0.161273300
## 36                        0.340812400                        0.221323200
## 37                        0.254517650                        0.255575135
## 38                        0.188937795                        0.133122850
## 39                        0.019569800                       -0.163281300
## 40                       -0.120443400                        0.079855700
## 41                        0.297834500                        0.227443290
## 42                        0.139287700                        0.138496000
## 43                        0.267307450                        0.165803350
## 44                        0.350515900                        0.366126100
## 45                        0.488397700                        0.552261100
## 46                        0.585015450                        0.557569000
## 47                        0.873091500                        0.452545900
## 48                        0.333805500                        0.080281000
## 49                        0.185748400                        0.182266900
## 50                        0.306603800                        0.250685050
## 51                        0.319815200                        0.241829850
## 52                        0.132895650                        0.079230358
## 53                        0.116260150                        0.243806790
## 54                        0.186574800                        0.127511350
## 55                        0.101181800                        0.009876250
## 56                        0.657859250                        0.517861000
## 57                        0.585332500                        0.350563750
## 58                        0.317365300                        0.281169100
## 59                        0.182547420                        0.303435100
## 60                        0.112322500                        0.241731500
## 61                        0.181221095                        0.199338050
## 62                        0.234502600                        0.184307350
## 63                        0.411186135                        0.370848195
## 64                        0.092486950                        0.118572600
## 65                        0.301801950                        0.344771700
## 66                        0.278571850                        0.233536700
## 67                        0.219394500                        0.179546400
## 68                        0.187634600                        0.311675700
## 69                       -0.117364300                       -0.071067500
## 70                        0.306686750                        0.244049800
## 71                        0.146805700                        0.119191650
## 72                        0.247347300                        0.259512250
## 73                        0.228546114                        0.191616300
## 74                        0.328522100                        0.259925550
## 75                        0.149618100                        0.145227890
## 76                        0.046892100                       -0.072370350
## 77                        0.586400000                        0.343332250
## 78                       -0.052637685                       -0.027981480
## 79                        0.324960705                        0.354993550
## 80                        0.175962100                        0.192482350
## 81                        0.359103000                        0.139323750
## 82                       -0.037849150                        0.136309650
## 83                        0.096365700                        0.127942600
## 84                       -0.032769165                       -0.053613150
## 85                        0.359254300                        0.238361250
## 86                        0.252011825                        0.243880650
## 87                        0.178403370                        0.216144500
## 88                        0.149480300                        0.136103600
## 89                        0.095604450                        0.121349100
## 90                       -0.041563000                       -0.116458400
## 91                        0.003737100                       -0.163873910
## 92                        0.224207593                        0.224967065
## 93                        0.676091150                        0.593536450
## 94                        0.180784300                        0.191811111
## 95                        0.666664885                        0.583749000
## 96                        0.377990570                        0.366306350
## 97                       -0.233521400                       -0.051788900
## 98                        0.224400475                        0.265794795
## 99                        0.412330300                        0.364387935
## 100                      -0.096859250                        0.078043100
## 101                       0.211591138                        0.160594150
## 102                       0.335796000                        0.233565250
## 103                       0.582640000                        0.360260600
## 104                       0.427764900                        0.350401300
## 105                       0.242959400                        0.057317495
## 106                       0.147332450                        0.110175740
## 107                       0.660153350                        0.527769000
## 108                       0.246288800                        0.049983600
## 109                       0.244925050                        0.049891600
## 110                       0.048897000                       -0.244031850
## 111                       0.270092200                        0.264217935
## 112                       0.126131650                       -0.036238870
## 113                      -0.067426500                        0.134911400
## 114                       0.229084900                        0.217894195
## 115                       0.120907850                        0.150399100
## 116                       0.155671674                        0.059902460
## 117                       0.151539500                        0.131969800
## 118                       0.141990350                        0.059375450
## 119                       0.666393650                        0.559337500
## 120                       0.131467800                        0.086897695
## 121                       0.200874350                        0.022444650
## 122                       0.178792100                        0.037895555
## 123                       0.270885305                        0.225862100
## 124                       0.142490935                        0.112436450
## 125                       0.196153350                        0.160321735
## 126                       0.134389650                        0.063467700
## 127                       0.228242450                        0.161273300
## 128                       0.184615700                        0.223358650
## 129                      -0.025335725                       -0.050877350
## 130                       0.314839250                        0.280839250
## 131                      -0.239801600                       -0.100257520
## 132                       0.165307205                        0.134408650
## 133                      -0.100287000                       -0.079264050
## 134                       0.880221500                        0.452966500
## 135                       0.243059300                        0.051025500
## 136                       0.370836200                        0.240345320
## 137                      -0.071657600                        0.046999450
## 138                       0.286351600                        0.254137550
## 139                       0.297834500                        0.227443290
## 140                      -0.129172800                        0.042388350
## 141                       0.163731700                        0.145174000
## 142                       0.191090150                        0.157252100
## 143                       0.172921650                        0.205421290
## 144                      -0.119248150                       -0.165040200
## 145                       0.333070335                        0.297296350
## 146                       0.060719400                       -0.029341300
## 147                       0.225493450                        0.189767700
## 148                      -0.208910550                       -0.088921500
## 149                      -0.096859250                        0.078043100
## 150                       0.335796000                        0.233565250
## 151                       0.008197900                       -0.082108350
## 152                       0.097797900                        0.137290550
## 153                       0.026596005                       -0.104232350
## 154                       0.224207593                        0.224967065
## 155                       0.117663400                        0.242223455
## 156                       0.076087500                       -0.068736400
## 157                       0.003403300                       -0.129461200
## 158                       0.244925050                        0.049891600
## 159                       0.184453815                        0.233430820
## 160                       0.122092800                        0.023663025
## 161                      -0.055903250                        0.067634100
## 162                       0.077739334                        0.058884205
## 163                       0.002409350                        0.049854800
## 164                      -0.170696200                       -0.232212650
## 165                       0.142767750                        0.131062200
## 166                       0.210305505                        0.216183510
## 167                       0.405615250                        0.359612350
## 168                       0.153853700                        0.023526235
## 169                       0.665210335                        0.571081400
## 170                      -0.209196450                        0.102301000
## 171                       0.046108000                        0.208286800
## 172                       0.134389650                        0.063467700
## 173                      -0.009305500                        0.050381350
## 174                       0.175515400                        0.093416500
## 175                      -0.252524300                       -0.074906900
## 176                      -0.022583205                        0.063529450
## 177                       0.267307450                        0.165803350
## 178                      -0.026720000                       -0.124274350
## 179                      -0.157575300                       -0.050144900
## 180                       0.122451900                        0.023086400
## 181                      -0.057834250                        0.067184350
## 182                       0.316623080                        0.276342950
## 183                      -0.153518500                        0.076305195
## 184                       0.146836700                        0.119661400
## 185                       0.024824600                       -0.072602850
## 186                       0.227583350                        0.184532750
## 187                       0.228395550                        0.038335200
## 188                       0.102642500                        0.141533950
## 189                      -0.128415300                       -0.178862700
## 190                       0.117420000                        0.245182015
## 191                      -0.038088890                       -0.057721060
## 192                      -0.064734700                        0.074282850
## 193                      -0.042767700                        0.021857570
## 194                       0.270885305                        0.225862100
## 195                       0.310256650                        0.284856100
## 196                       0.189325900                        0.295528300
## 197                      -0.258895200                       -0.078346950
## 198                      -0.027155950                        0.043923180
## 199                      -0.160664800                       -0.191736500
## 200                       0.099017350                        0.053445300
## 201                      -0.015402350                        0.039398250
## 202                       0.134576215                        0.082354950
## 203                       0.318699600                        0.363359980
## 204                       0.163852000                        0.135358515
## 205                      -0.250127250                       -0.125335260
## 206                       0.196563400                        0.021562150
## 207                       0.427813800                        0.356573675
## 208                       0.020024000                        0.136790700
## 209                       0.227583350                        0.184532750
## 210                      -0.231810500                       -0.217176550
## 211                       0.227535800                        0.152684125
## 212                      -0.032769165                       -0.053613150
## 213                       0.135280600                        0.114997330
## 214                       0.163964850                        0.081467600
## 215                       0.163816830                       -0.085953300
## 216                      -0.203113100                       -0.093104850
## 217                      -0.063569680                        0.123876650
## 218                       0.134576215                        0.082354950
## 219                       0.127749900                        0.062852150
## 220                       0.177507000                        0.187841000
## 221                       0.370836200                        0.240345320
## 222                      -0.055541250                        0.063773815
## 223                      -0.037092150                       -0.046280900
## 224                       0.127048800                       -0.015174750
## 225                       0.124527400                        0.028159450
## 226                       0.225343650                        0.184115100
## 227                      -0.019655600                        0.030571215
## 228                       0.213909750                        0.140456700
## 229                       0.047253450                        0.100313600
## 230                       0.243650550                        0.051252500
## 231                       0.145816645                        0.070187500
## 232                       0.146491550                        0.074906840
## 233                       0.225874900                        0.147307830
## 234                       0.008431850                        0.061213200
## 235                       0.184221950                        0.022793315
## 236                       0.044142200                        0.022037575
## 237                       0.359708000                        0.135557350
## 238                       0.333805500                        0.080281000
## 239                      -0.085413350                       -0.173800500
## 240                       0.150761300                        0.178193150
## 241                       0.462506000                        0.576412550
## 242                      -0.021073400                       -0.104186000
## 243                      -0.058048105                       -0.051322150
## 244                       0.093547546                       -0.060639700
## 245                      -0.139794685                       -0.080961650
## 246                       0.147332450                        0.110175740
## 247                       0.333070335                        0.297296350
## 248                       0.019947150                        0.195527100
## 249                       0.128302550                        0.056433900
## 250                       0.120950550                        0.243639945
## 251                       0.000105500                       -0.167453025
## 252                       0.100323300                       -0.084936675
## 253                       0.179721550                        0.241952800
## 254                       0.381828250                        0.216791150
## 255                       0.069251850                        0.065002250
## 256                       0.037842100                       -0.066596150
## 257                      -0.001347500                        0.043069985
## 258                       0.178045915                        0.177698500
## 259                       0.304765600                        0.335966430
## 260                       0.110483750                        0.046759000
## 261                       0.245897470                        0.225517800
## 262                       0.359103000                        0.139323750
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## 697                      -0.249175650                       -0.129839300
## 698                      -0.055298698                       -0.052335350
## 699                      -0.081399451                        0.034635675
## 700                       0.245484250                        0.236135030
## 701                       0.033199150                        0.126414820
## 702                       0.004329800                       -0.068982950
## 703                      -0.054586800                        0.155356700
## 704                      -0.029192650                       -0.116595750
## 705                      -0.061296400                       -0.020084820
## 706                      -0.018199000                       -0.084745710
## 707                      -0.026437000                       -0.126213350
## 708                       0.058894800                       -0.036311200
## 709                       0.219871350                        0.231582700
## 710                      -0.029444000                       -0.095704300
## 711                       0.026016240                       -0.098620130
## 712                       0.261007700                        0.253497750
## 713                      -0.222213200                       -0.145922950
## 714                      -0.201983400                       -0.192071500
## 715                      -0.166507000                       -0.039085300
## 716                       0.020943100                        0.138933000
## 717                       0.037745150                        0.129007500
## 718                      -0.067426500                        0.134911400
## 719                       0.060260500                       -0.067249350
## 720                      -0.040983200                        0.145903939
## 721                      -0.023406345                        0.027538255
## 722                       0.029412500                        0.195851650
## 723                       0.314839250                        0.280839250
## 724                       0.094539400                        0.038592300
## 725                      -0.065830550                       -0.054155750
## 726                      -0.005544000                       -0.118667060
## 727                      -0.232407550                        0.101165500
## 728                       0.337440240                        0.223071650
## 729                      -0.055194600                       -0.220780015
## 730                       0.405615250                        0.359612350
## 731                       0.134667200                        0.118204130
## 732                       0.193055745                        0.156230005
## 733                       0.149480300                        0.136103600
## 734                      -0.177943210                       -0.059864350
## 735                       0.373497050                        0.232372700
## 736                       0.102989050                       -0.077549957
## 737                      -0.109081900                        0.122113180
## 738                      -0.038877500                        0.242950600
## 739                      -0.027245350                       -0.098154165
## 740                       0.248817300                        0.060705200
## 741                      -0.167480700                       -0.184949650
## 742                       0.003854200                       -0.061420550
## 743                       0.061434400                       -0.054431360
## 744                      -0.042767700                        0.021857570
## 745                       0.178045915                        0.177698500
## 746                       0.004530500                        0.134995650
## 747                       0.102519750                        0.140533900
## 748                       0.102519750                        0.140533900
## 749                       0.093976250                       -0.063508275
## 750                      -0.109081900                        0.122113180
## 751                      -0.152885050                       -0.285186800
## 752                       0.125735750                        0.081142050
## 753                       0.373497050                        0.232372700
## 754                      -0.007850900                       -0.113459800
## 755                      -0.040586000                        0.170927900
## 756                       0.245484250                        0.236135030
## 757                       0.004231750                       -0.057513800
## 758                       0.337881850                        0.227910200
## 759                       0.028828500                       -0.080344595
## 760                      -0.041186500                        0.049304920
## 761                       0.008674050                        0.112087150
## 762                      -0.206748250                       -0.081147700
## 763                       0.246288800                        0.049983600
## 764                      -0.102317700                       -0.078306250
## 765                       0.113455200                       -0.062299900
## 766                      -0.246176850                       -0.119130250
## 767                       0.227583350                        0.184532750
## 768                       0.095604450                        0.121349100
## 769                       0.056773000                       -0.246783400
## 770                      -0.134717950                       -0.079895000
## 771                      -0.125930900                       -0.179949300
## 772                       0.061226800                        0.070390300
## 773                      -0.142462300                       -0.114928865
## 774                       0.060066950                       -0.235061550
## 775                       0.222948450                        0.142438800
## 776                       0.094105200                        0.118618550
## 777                       0.130596800                        0.054589200
## 778                       0.151877750                        0.176222450
## 779                       0.048897000                       -0.244031850
## 780                       0.152682450                        0.156648850
## 781                      -0.150480550                       -0.046625100
## 782                      -0.160664800                       -0.191736500
## 783                       0.149176900                        0.129438320
## 784                       0.149828050                        0.162439950
## 785                       0.037745150                        0.129007500
## 786                      -0.066455835                       -0.048643150
## 787                       0.068208750                       -0.061682800
## 788                       0.135280600                        0.114997330
## 789                       0.484295000                        0.536037200
## 790                       0.107300050                        0.090858750
## 791                      -0.191732300                       -0.162263250
## 792                      -0.240719950                       -0.092261050
## 793                       0.064611550                       -0.046072150
## 794                       0.178529850                        0.193648300
## 795                       0.076087500                       -0.068736400
## 796                      -0.187420750                       -0.198625400
## 797                       0.177507000                        0.187841000
## 798                       0.339001700                        0.240743850
## 799                       0.060260500                       -0.067249350
## 800                       0.147133100                        0.155591580
## 801                       0.184183500                        0.024717600
## 802                      -0.052637685                       -0.027981480
## 803                      -0.260245100                       -0.071917150
## 804                       0.180784300                        0.191811111
## 805                      -0.011280500                       -0.105622025
## 806                       0.029661180                       -0.078261755
## 807                       0.320669650                        0.137588700
## 808                       0.048081500                       -0.288418845
## 809                      -0.227815145                        0.071897600
## 810                      -0.032823050                       -0.102628300
## 811                       0.129525150                       -0.075214050
## 812                       0.143252300                        0.095120300
## 813                       0.002959385                       -0.067890600
##     posterior_median_hard_skill_loser lower.025_q_clay_skill_loser
## 1                        6.204545e-01                  0.466121175
## 2                        5.512985e-01                  0.733955625
## 3                        6.966490e-01                  0.599196522
## 4                        9.731970e-02                 -0.170001830
## 5                        2.981105e-01                  0.250351070
## 6                        2.205305e-02                 -0.164517567
## 7                        6.501285e-01                  0.545267885
## 8                        1.910300e-01                  0.137789325
## 9                        3.264215e-02                 -0.077785462
## 10                       5.711375e-01                  0.379336425
## 11                       5.677305e-01                  0.780558200
## 12                       3.031795e-01                  0.276042330
## 13                       2.005225e-01                 -0.003730263
## 14                       5.531815e-01                  0.756174650
## 15                       2.172840e-01                  0.130419290
## 16                       5.897130e-01                  0.374815875
## 17                       5.639370e-01                  0.801524925
## 18                       4.083390e-01                  0.503615625
## 19                       6.697735e-01                  0.564079147
## 20                       1.135770e-01                 -0.058385862
## 21                       1.295320e-01                  0.065186110
## 22                       3.372160e-01                  0.200381000
## 23                       2.864820e-01                  0.116124740
## 24                       1.613990e-01                  0.045876550
## 25                       2.108635e-01                  0.089931020
## 26                      -5.201380e-02                 -0.240296395
## 27                      -1.064190e-01                 -0.081085122
## 28                       5.521880e-01                  0.761019575
## 29                       2.172840e-01                  0.130419290
## 30                       2.911355e-01                  0.155333365
## 31                       1.935950e-01                  0.081821130
## 32                       1.545375e-01                  0.063093913
## 33                       2.346135e-01                  0.078726825
## 34                       2.751865e-01                  0.107017475
## 35                       1.900425e-01                  0.088055717
## 36                       2.843195e-01                  0.249274240
## 37                       2.878725e-01                  0.120781250
## 38                       1.488915e-01                  0.063993817
## 39                      -1.493540e-01                 -0.066350575
## 40                       5.115300e-02                 -0.246818260
## 41                       2.804455e-01                  0.198041191
## 42                       1.746885e-01                  0.012186210
## 43                       2.048800e-01                  0.143489587
## 44                       3.611050e-01                  0.245452933
## 45                       5.841570e-01                  0.382199675
## 46                       6.330165e-01                  0.492171750
## 47                       5.646110e-01                  0.794108075
## 48                       1.517730e-01                  0.260878277
## 49                       2.264025e-01                  0.080877075
## 50                       3.338710e-01                  0.213670425
## 51                       2.657780e-01                  0.212249688
## 52                       9.028170e-02                  0.044232972
## 53                       2.187400e-01                  0.012852000
## 54                       1.398695e-01                  0.067284214
## 55                       3.675860e-02                 -0.044343143
## 56                       6.474895e-01                  0.543422602
## 57                       4.138470e-01                  0.507775243
## 58                       3.347630e-01                  0.219981838
## 59                       2.324755e-01                  0.037446700
## 60                       2.156625e-01                 -0.017901000
## 61                       2.259140e-01                  0.078642725
## 62                       2.128990e-01                  0.135524625
## 63                       3.932785e-01                  0.321017743
## 64                       1.046835e-01                 -0.050639823
## 65                       3.608930e-01                  0.184409575
## 66                       2.857695e-01                  0.162521550
## 67                       2.387110e-01                  0.135029380
## 68                       2.320605e-01                  0.031194500
## 69                      -8.316105e-02                 -0.391661760
## 70                       3.382850e-01                  0.194267225
## 71                       1.402315e-01                  0.035842087
## 72                       2.957255e-01                  0.112709800
## 73                       2.549015e-01                  0.134376620
## 74                       2.827325e-01                  0.222248000
## 75                       1.205380e-01                  0.043058570
## 76                      -7.848295e-02                 -0.031391510
## 77                       4.100815e-01                  0.506006488
## 78                      -1.754210e-02                 -0.322242073
## 79                       3.646810e-01                  0.223413350
## 80                       2.513160e-01                  0.065769275
## 81                       1.869855e-01                  0.289804250
## 82                       7.656255e-02                 -0.162460495
## 83                       1.135770e-01                 -0.058385862
## 84                      -4.287630e-02                 -0.288937728
## 85                       2.984370e-01                  0.279857173
## 86                       2.807425e-01                  0.157856532
## 87                       2.312555e-01                  0.089318647
## 88                       1.853220e-01                  0.015804475
## 89                       1.050175e-01                 -0.054744030
## 90                      -1.290420e-01                 -0.168390432
## 91                      -1.425630e-01                 -0.085208110
## 92                       2.193420e-01                  0.134046184
## 93                       6.923225e-01                  0.585612440
## 94                       2.153505e-01                  0.076363500
## 95                       6.856270e-01                  0.576100648
## 96                       3.807820e-01                  0.286804958
## 97                      -1.254740e-01                 -0.410338223
## 98                       2.813155e-01                  0.066603450
## 99                       3.922250e-01                  0.323576198
## 100                      5.758620e-02                 -0.212892189
## 101                      1.899155e-01                  0.070602000
## 102                      2.935390e-01                  0.245422417
## 103                      4.352855e-01                  0.510883048
## 104                      3.763735e-01                  0.334968058
## 105                      1.434190e-01                  0.141105045
## 106                      1.550720e-01                  0.061354287
## 107                      6.508680e-01                  0.550151857
## 108                      1.358675e-01                  0.141837910
## 109                      1.486700e-01                  0.144510457
## 110                     -1.833965e-01                 -0.049895210
## 111                      3.015560e-01                  0.152527632
## 112                      1.725310e-03                  0.012745718
## 113                      6.247785e-02                 -0.218202620
## 114                      2.068590e-01                  0.144263423
## 115                      1.797790e-01                 -0.009646850
## 116                      6.365910e-02                  0.060362688
## 117                      1.558555e-01                  0.045561673
## 118                      1.036575e-01                  0.026339222
## 119                      6.727980e-01                  0.571886015
## 120                      9.589280e-02                  0.039332752
## 121                      1.018140e-01                  0.061135708
## 122                      9.204605e-02                  0.051859055
## 123                      2.827530e-01                  0.159423615
## 124                      1.545375e-01                  0.063093913
## 125                      1.760580e-01                  0.099128367
## 126                      9.544630e-02                 -0.048662268
## 127                      1.900425e-01                  0.088055717
## 128                      2.589165e-01                  0.086744875
## 129                     -5.201380e-02                 -0.240296395
## 130                      3.309335e-01                  0.226458400
## 131                     -1.504235e-01                 -0.437790725
## 132                      1.390375e-01                  0.029895815
## 133                     -1.035360e-01                 -0.265043858
## 134                      5.794295e-01                  0.799272000
## 135                      1.505670e-01                  0.142746637
## 136                      3.040595e-01                  0.293604025
## 137                      4.525930e-02                 -0.225269575
## 138                      2.661605e-01                  0.171828360
## 139                      2.804455e-01                  0.198041191
## 140                      1.163780e-02                 -0.341002712
## 141                      1.272845e-01                  0.071534502
## 142                      1.935950e-01                  0.081821130
## 143                      2.242585e-01                  0.048116450
## 144                     -1.686475e-01                 -0.421994298
## 145                      3.161070e-01                  0.244226058
## 146                     -7.830225e-03                 -0.171733810
## 147                      2.123300e-01                  0.124853825
## 148                     -1.377570e-01                 -0.419747700
## 149                      5.758620e-02                 -0.212892189
## 150                      2.935390e-01                  0.245422417
## 151                     -7.827550e-02                 -0.166558465
## 152                      1.272005e-01                 -0.059331250
## 153                     -8.598805e-02                 -0.176679685
## 154                      2.193420e-01                  0.134046184
## 155                      2.200075e-01                  0.012986550
## 156                     -3.684355e-02                 -0.022973432
## 157                     -1.107025e-01                 -0.091606315
## 158                      1.486700e-01                  0.144510457
## 159                      2.715280e-01                  0.088945500
## 160                      4.177210e-02                  0.019795463
## 161                      5.809905e-02                 -0.235303056
## 162                      5.406400e-02                 -0.031937610
## 163                      5.280415e-02                 -0.245175375
## 164                     -2.450890e-01                 -0.333110837
## 165                      1.714080e-01                  0.012762700
## 166                      2.055445e-01                  0.121771692
## 167                      3.907545e-01                  0.313323115
## 168                      4.004300e-02                  0.075900092
## 169                      6.820920e-01                  0.571501805
## 170                      2.241230e-02                 -0.394230904
## 171                      1.703200e-01                 -0.090907308
## 172                      9.544630e-02                 -0.048662268
## 173                      4.626995e-02                 -0.194687590
## 174                      1.257515e-01                 -0.016476158
## 175                     -9.610740e-02                 -0.470215093
## 176                      7.187045e-02                 -0.156996888
## 177                      2.048800e-01                  0.143489587
## 178                     -1.375795e-01                 -0.165949100
## 179                     -1.278640e-01                 -0.317749465
## 180                      4.503230e-02                  0.018159545
## 181                      4.283265e-02                 -0.232735055
## 182                      3.334095e-01                  0.223626097
## 183                      1.290075e-02                 -0.388416553
## 184                      1.396875e-01                  0.026961060
## 185                     -9.763025e-02                 -0.060814250
## 186                      2.512240e-01                  0.134362275
## 187                      1.176215e-01                  0.131393618
## 188                      1.336345e-01                 -0.049571225
## 189                     -1.861845e-01                 -0.305679582
## 190                      2.219320e-01                  0.012948625
## 191                     -5.200760e-02                 -0.281735875
## 192                      2.657965e-02                 -0.352807970
## 193                      2.875850e-02                 -0.168626738
## 194                      2.827530e-01                  0.159423615
## 195                      3.369430e-01                  0.214309250
## 196                      2.242345e-01                  0.054608958
## 197                     -9.491095e-02                 -0.468580070
## 198                      2.364060e-02                 -0.167214815
## 199                     -2.089555e-01                 -0.354049080
## 200                      4.297550e-02                 -0.062853553
## 201                      9.151320e-03                 -0.142385778
## 202                      8.803435e-02                  0.032420705
## 203                      3.783345e-01                  0.213514400
## 204                      1.621155e-01                  0.064885775
## 205                     -1.768840e-01                 -0.482557100
## 206                      9.378670e-02                  0.058704343
## 207                      3.778245e-01                  0.335484608
## 208                      1.453035e-01                 -0.100979793
## 209                      2.512240e-01                  0.134362275
## 210                     -2.475170e-01                 -0.527050300
## 211                      1.782570e-01                  0.086104192
## 212                     -4.287630e-02                 -0.288937728
## 213                      1.337750e-01                  0.018392200
## 214                      1.235785e-01                 -0.001884200
## 215                     -4.311450e-02                  0.078657670
## 216                     -1.361405e-01                 -0.417669800
## 217                      6.231560e-02                 -0.221131900
## 218                      8.803435e-02                  0.032420705
## 219                      8.946125e-02                 -0.057548848
## 220                      2.108960e-01                  0.082154300
## 221                      3.040595e-01                  0.293604025
## 222                      5.683435e-02                 -0.242224583
## 223                     -2.931260e-02                 -0.160782115
## 224                      1.359275e-02                 -0.008845555
## 225                      4.963125e-02                  0.022550790
## 226                      2.462870e-01                  0.136201925
## 227                      2.347995e-02                 -0.277093715
## 228                      1.638600e-01                  0.092761968
## 229                      1.194605e-01                 -0.083560275
## 230                      1.485215e-01                  0.139900661
## 231                      1.119880e-01                  0.031550921
## 232                      1.148085e-01                  0.031870550
## 233                      1.730295e-01                  0.078808865
## 234                      7.476335e-02                 -0.194667518
## 235                      4.246420e-02                  0.097184232
## 236                      4.638425e-02                 -0.124947523
## 237                      1.787955e-01                  0.289119875
## 238                      1.517730e-01                  0.260878277
## 239                     -1.815200e-01                 -0.237954179
## 240                      2.182375e-01                  0.030117150
## 241                      5.814530e-01                  0.359341725
## 242                     -7.144300e-02                 -0.271454900
## 243                     -3.980210e-02                 -0.330397225
## 244                     -3.231265e-02                 -0.008957973
## 245                     -1.116005e-01                 -0.330910800
## 246                      1.550720e-01                  0.061354287
## 247                      3.161070e-01                  0.244226058
## 248                      1.522145e-01                 -0.104888475
## 249                      4.852385e-02                 -0.001276568
## 250                      2.305625e-01                  0.007595625
## 251                     -1.518230e-01                 -0.092898798
## 252                     -3.561105e-02                 -0.003559885
## 253                      2.727390e-01                  0.080042175
## 254                      3.297195e-01                  0.299084208
## 255                      7.966730e-02                 -0.202441510
## 256                     -8.073125e-02                 -0.039489122
## 257                      3.513385e-02                 -0.228560288
## 258                      2.249615e-01                  0.075160625
## 259                      3.541000e-01                  0.185249425
## 260                      7.665900e-02                 -0.088986992
## 261                      2.844090e-01                  0.136419300
## 262                      1.869855e-01                  0.289804250
## 263                      1.485215e-01                  0.139900661
## 264                      2.346135e-01                  0.078726825
## 265                     -8.097600e-02                 -0.110105723
## 266                     -1.721540e-01                 -0.488424425
## 267                     -1.231515e-01                 -0.307104225
## 268                      1.693155e-02                 -0.296305920
## 269                      6.964935e-02                  0.019917377
## 270                      1.774630e-01                 -0.190362460
## 271                      3.015615e-01                  0.116536650
## 272                      4.289160e-02                 -0.035825112
## 273                      2.186520e-01                  0.085466750
## 274                     -1.409085e-01                 -0.157891068
## 275                     -1.669710e-02                 -0.165255915
## 276                     -9.572755e-02                 -0.224228120
## 277                      6.250460e-02                 -0.207195382
## 278                     -9.758505e-02                 -0.142100685
## 279                      2.526505e-01                  0.125544960
## 280                     -1.348660e-02                 -0.333080077
## 281                      1.708980e-01                 -0.094735525
## 282                      4.219445e-02                 -0.206028255
## 283                     -1.016000e-01                 -0.393524730
## 284                     -6.075950e-02                  0.039983997
## 285                     -6.343655e-02                 -0.353435535
## 286                      7.723325e-02                 -0.214221500
## 287                     -1.198325e-01                 -0.172598793
## 288                     -5.288260e-02                 -0.187818955
## 289                     -3.397310e-02                 -0.115602608
## 290                      6.971810e-02                 -0.220019620
## 291                      3.807820e-01                  0.286804958
## 292                      1.649280e-01                  0.034260825
## 293                      1.899155e-01                  0.070602000
## 294                      2.603765e-02                 -0.218291955
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## 687                     -5.608750e-02                 -0.017115775
## 688                     -1.266445e-01                 -0.483382050
## 689                      1.202870e-02                 -0.393232587
## 690                     -1.504235e-01                 -0.437790725
## 691                     -7.874875e-02                 -0.092027535
## 692                     -1.954495e-01                 -0.010747750
## 693                     -8.319785e-02                 -0.451720075
## 694                      8.178925e-02                  0.021644872
## 695                     -1.518230e-01                 -0.092898798
## 696                      9.355745e-02                  0.055375636
## 697                     -1.965495e-01                 -0.427212437
## 698                     -3.953365e-02                 -0.179307192
## 699                      2.537220e-02                 -0.237076322
## 700                      2.980475e-01                  0.131947625
## 701                      1.418095e-01                 -0.078850147
## 702                     -8.964815e-02                 -0.118422157
## 703                      9.500910e-02                 -0.210779743
## 704                     -1.345865e-01                 -0.155899129
## 705                     -1.633860e-02                 -0.288857798
## 706                     -8.127840e-02                 -0.209227550
## 707                     -1.388550e-01                 -0.157560016
## 708                     -1.867360e-02                 -0.167110908
## 709                      2.751865e-01                  0.107017475
## 710                     -9.732015e-02                 -0.160128835
## 711                     -8.819500e-02                 -0.172470135
## 712                      2.904715e-01                  0.122965850
## 713                     -1.957145e-01                 -0.424738150
## 714                     -2.011720e-01                 -0.408925658
## 715                     -7.459445e-02                 -0.412526600
## 716                      9.496620e-02                 -0.070366978
## 717                      1.465090e-01                 -0.077046525
## 718                      6.247785e-02                 -0.218202620
## 719                     -8.161985e-02                 -0.059423468
## 720                      7.187520e-02                 -0.164935178
## 721                      3.852840e-02                 -0.154578838
## 722                      1.617140e-01                 -0.097348298
## 723                      3.309335e-01                  0.226458400
## 724                      5.122530e-02                 -0.008830160
## 725                     -5.931025e-02                 -0.355955905
## 726                     -1.001960e-01                 -0.142018513
## 727                      1.669800e-02                 -0.397460330
## 728                      2.800640e-01                  0.251354296
## 729                     -1.981790e-01                 -0.170322958
## 730                      3.907545e-01                  0.313323115
## 731                      1.355625e-01                  0.013028820
## 732                      1.894080e-01                  0.089145440
## 733                      1.853220e-01                  0.015804475
## 734                     -9.815410e-02                 -0.352715020
## 735                      3.003810e-01                  0.297129795
## 736                     -2.536335e-02                 -0.075766957
## 737                      1.991290e-02                 -0.316059555
## 738                      1.425045e-01                 -0.204060985
## 739                     -7.530165e-02                 -0.302359265
## 740                      1.428050e-01                  0.142060900
## 741                     -2.095060e-01                 -0.323790285
## 742                     -8.351940e-02                 -0.117353250
## 743                     -6.793145e-02                 -0.060168937
## 744                      2.875850e-02                 -0.168626738
## 745                      2.249615e-01                  0.075160625
## 746                      1.089785e-01                 -0.178457235
## 747                      1.293390e-01                 -0.043176975
## 748                      1.293390e-01                 -0.043176975
## 749                     -3.052180e-02                 -0.012786055
## 750                      1.991290e-02                 -0.316059555
## 751                     -3.019510e-01                 -0.277906767
## 752                      9.506325e-02                  0.042101515
## 753                      3.003810e-01                  0.297129795
## 754                     -9.565220e-02                 -0.147119940
## 755                      7.701020e-02                 -0.212270388
## 756                      2.980475e-01                  0.131947625
## 757                     -8.009180e-02                 -0.115764293
## 758                      2.860095e-01                  0.249629106
## 759                     -9.907230e-02                 -0.048218400
## 760                      3.668455e-02                 -0.250971260
## 761                      9.731970e-02                 -0.170001830
## 762                     -1.376935e-01                 -0.413117375
## 763                      1.358675e-01                  0.141837910
## 764                     -1.052870e-01                 -0.265677408
## 765                     -6.075950e-02                  0.039983997
## 766                     -1.721540e-01                 -0.488424425
## 767                      2.512240e-01                  0.134362275
## 768                      1.050175e-01                 -0.054744030
## 769                     -1.727455e-01                 -0.043601550
## 770                     -9.288085e-02                 -0.279428285
## 771                     -1.876785e-01                 -0.295849185
## 772                      9.752210e-02                 -0.105563698
## 773                     -1.356820e-01                 -0.367964745
## 774                     -1.647160e-01                 -0.034234150
## 775                      1.642680e-01                  0.073097400
## 776                      1.063305e-01                 -0.057417937
## 777                      8.208255e-02                 -0.080512505
## 778                      2.240175e-01                  0.027901225
## 779                     -1.833965e-01                 -0.049895210
## 780                      1.337595e-01                  0.046002878
## 781                     -7.687365e-02                 -0.360821993
## 782                     -2.089555e-01                 -0.354049080
## 783                      1.365790e-01                  0.004977450
## 784                      1.298955e-01                  0.030627852
## 785                      1.465090e-01                 -0.077046525
## 786                     -4.060475e-02                 -0.339261045
## 787                     -7.248560e-02                 -0.007954608
## 788                      1.337750e-01                  0.018392200
## 789                      5.761685e-01                  0.378225100
## 790                      1.101125e-01                 -0.251524317
## 791                     -1.915275e-01                 -0.471410950
## 792                     -1.408675e-01                 -0.434103500
## 793                     -5.328455e-02                 -0.054835590
## 794                      2.185490e-01                  0.081109782
## 795                     -3.684355e-02                 -0.022973432
## 796                     -2.219470e-01                 -0.393676608
## 797                      2.108960e-01                  0.082154300
## 798                      3.149745e-01                  0.255456217
## 799                     -8.161985e-02                 -0.059423468
## 800                      1.321515e-01                  0.025263442
## 801                      9.355745e-02                  0.055375636
## 802                     -1.754210e-02                 -0.322242073
## 803                     -9.467400e-02                 -0.475243085
## 804                      2.153505e-01                  0.076363500
## 805                     -1.305015e-01                 -0.135169527
## 806                     -1.012215e-01                 -0.050129810
## 807                      1.936040e-01                  0.241997140
## 808                     -2.089075e-01                 -0.061513900
## 809                      3.997895e-03                 -0.384652083
## 810                     -9.572755e-02                 -0.224228120
## 811                     -5.678675e-02                  0.013807012
## 812                      8.513215e-02                  0.063551032
## 813                     -6.561330e-02                 -0.156100983
##     lower.025_q_grass_skill_loser lower.025_q_hard_skill_loser
## 1                    0.4109353750                 0.5425691500
## 2                    0.3262893000                 0.4821160250
## 3                    0.4963900000                 0.6393150000
## 4                   -0.0503296112                -0.0172218900
## 5                    0.1152751000                 0.2300226750
## 6                   -0.1280681623                -0.0742335000
## 7                    0.4041353250                 0.5834753500
## 8                    0.0398094000                 0.1089697500
## 9                   -0.1984648950                -0.1252568500
## 10                   0.4272502250                 0.5065870000
## 11                   0.3150262500                 0.5039058750
## 12                   0.1834002575                 0.2476187750
## 13                   0.0199511275                 0.0756215925
## 14                   0.3175032500                 0.4806573000
## 15                   0.1132241425                 0.1484200250
## 16                   0.4600306250                 0.5273604250
## 17                   0.3447489750                 0.4972012000
## 18                   0.2243403750                 0.3385108500
## 19                   0.4574988500                 0.6080192250
## 20                  -0.0019870450                 0.0239892000
## 21                  -0.0760947925                 0.0360317000
## 22                   0.1705996000                 0.2694633000
## 23                   0.1163271250                 0.2029789500
## 24                   0.0327770000                 0.0881433200
## 25                   0.0840494875                 0.1556222250
## 26                  -0.2353386600                -0.2089540250
## 27                  -0.2941632000                -0.2246371750
## 28                   0.3128496000                 0.4825190750
## 29                   0.1132241425                 0.1484200250
## 30                   0.1219581775                 0.2221096750
## 31                   0.0478054250                 0.1288060250
## 32                   0.0049198500                 0.0895421600
## 33                   0.0873841000                 0.1711718500
## 34                   0.1071312250                 0.2106460750
## 35                   0.0477939725                 0.1105738250
## 36                   0.0938957250                 0.2033408250
## 37                   0.1336910500                 0.2078788000
## 38                   0.0209117173                 0.0683097800
## 39                  -0.3086617250                -0.2481362500
## 40                  -0.0593708825                -0.0290697400
## 41                   0.0919670750                 0.2010993500
## 42                   0.0072156500                 0.0969992375
## 43                   0.0543344750                 0.1363491750
## 44                   0.2458633100                 0.2950194000
## 45                   0.4531624250                 0.5178450250
## 46                   0.4630421000                 0.5726967000
## 47                   0.3419613000                 0.5000985500
## 48                  -0.0475343200                 0.0716968650
## 49                   0.0490419000                 0.1589592500
## 50                   0.0995430000                 0.2621877500
## 51                   0.1159687500                 0.1939151500
## 52                  -0.0307768850                 0.0187314275
## 53                   0.1489331675                 0.1579451250
## 54                   0.0154397600                 0.0552631200
## 55                  -0.1443161345                -0.0834189675
## 56                   0.4032251750                 0.5815101500
## 57                   0.2387427500                 0.3491500500
## 58                   0.1661501250                 0.2690580500
## 59                   0.1887787875                 0.1450384500
## 60                   0.1195543300                 0.1368981000
## 61                   0.0878542075                 0.1650880000
## 62                   0.0690130250                 0.1405927500
## 63                   0.2672851250                 0.3388758500
## 64                  -0.0136237975                -0.0044635840
## 65                   0.2285966625                 0.2968162250
## 66                   0.1157970000                 0.2200192500
## 67                   0.0666106750                 0.1771073500
## 68                   0.1888298725                 0.1397310500
## 69                  -0.2912736400                -0.2609523750
## 70                   0.0967138500                 0.2700454500
## 71                  -0.0252850500                 0.0573206825
## 72                   0.1281198525                 0.2020055000
## 73                   0.0702571250                 0.1851123000
## 74                   0.1448820025                 0.2097820250
## 75                   0.0423865575                 0.0528578100
## 76                  -0.1910120175                -0.1666216500
## 77                   0.2391333500                 0.3465523750
## 78                  -0.2090304100                -0.1791578750
## 79                   0.2561552875                 0.3021988500
## 80                   0.0615495500                 0.1787624750
## 81                   0.0266542550                 0.1181100000
## 82                   0.0281145975                -0.0017344080
## 83                  -0.0019870450                 0.0239892000
## 84                  -0.2423829025                -0.2025060750
## 85                   0.1265676850                 0.2292674750
## 86                   0.1204426500                 0.2215070000
## 87                   0.1116275550                 0.1728790750
## 88                   0.0074469750                 0.1106872000
## 89                   0.0020782450                 0.0109814160
## 90                  -0.2632799675                -0.2239292500
## 91                  -0.3215678250                -0.2478153250
## 92                   0.1282201500                 0.1487855500
## 93                   0.4988305000                 0.6412483500
## 94                   0.0828690750                 0.1583681250
## 95                   0.4837458000                 0.6287311750
## 96                   0.2711024675                 0.3239717000
## 97                  -0.1897306075                -0.2320203750
## 98                   0.0872378525                 0.1805590000
## 99                   0.2575284000                 0.3335590250
## 100                 -0.0465835380                -0.0174591925
## 101                  0.0502822075                 0.1159871250
## 102                  0.1095932600                 0.2214062750
## 103                  0.2571996175                 0.3708196000
## 104                  0.2468188500                 0.3140277750
## 105                 -0.1004303325                 0.0536472750
## 106                  0.0054888625                 0.0918789100
## 107                  0.4073429000                 0.5839465000
## 108                 -0.1026131500                 0.0419347525
## 109                 -0.1115632250                 0.0597233100
## 110                 -0.4214527000                -0.3156096000
## 111                  0.1419023625                 0.2235828500
## 112                 -0.1655892350                -0.0895152725
## 113                  0.0056332687                -0.0297878125
## 114                  0.1223107250                 0.1445054000
## 115                  0.0113371250                 0.1007130750
## 116                 -0.0442599500                -0.0170675475
## 117                  0.0072457500                 0.0660923900
## 118                 -0.0838220300                 0.0259468800
## 119                  0.4585638000                 0.6098572500
## 120                 -0.0344371425                 0.0207337775
## 121                 -0.1522406375                 0.0229365700
## 122                 -0.1079118875                 0.0153203675
## 123                  0.0988663000                 0.2066138000
## 124                  0.0049198500                 0.0895421600
## 125                  0.0351160125                 0.1056591750
## 126                 -0.1130805943                -0.0429104750
## 127                  0.0477939725                 0.1105738250
## 128                  0.1120241250                 0.1966783000
## 129                 -0.2353386600                -0.2089540250
## 130                  0.1816118000                 0.2648733500
## 131                 -0.2506725250                -0.2656446500
## 132                  0.0132393250                 0.0477655975
## 133                 -0.2413180375                -0.2444026750
## 134                  0.3421729750                 0.5167614500
## 135                 -0.1209146425                 0.0572721750
## 136                  0.1164159250                 0.2323127750
## 137                 -0.0740236700                -0.0430922075
## 138                  0.1081872175                 0.1870445500
## 139                  0.0919670750                 0.2010993500
## 140                 -0.0748016632                -0.0746318225
## 141                  0.0284800125                 0.0438844025
## 142                  0.0478054250                 0.1288060250
## 143                  0.0640223750                 0.1526200000
## 144                 -0.4415059075                -0.4166718250
## 145                  0.1826034575                 0.2567951500
## 146                 -0.1992375950                -0.1370686500
## 147                  0.0669471825                 0.1387792500
## 148                 -0.2471416075                -0.2630154000
## 149                 -0.0465835380                -0.0174591925
## 150                  0.1095932600                 0.2214062750
## 151                 -0.2619248950                -0.2251152000
## 152                  0.0138950700                 0.0393204500
## 153                 -0.3917232900                -0.3408836750
## 154                  0.1282201500                 0.1487855500
## 155                  0.1453634825                 0.1559678250
## 156                 -0.2435570975                -0.1594991750
## 157                 -0.3044280475                -0.2319299000
## 158                 -0.1115632250                 0.0597233100
## 159                  0.1245177500                 0.2011650000
## 160                 -0.1017876425                -0.0449531625
## 161                 -0.0590325250                -0.0252825675
## 162                 -0.0822892800                -0.0470298500
## 163                 -0.1202586075                -0.0526891450
## 164                 -0.4578468775                -0.4181465250
## 165                  0.0127119750                 0.0946239650
## 166                  0.1164451800                 0.1400514750
## 167                  0.2665046200                 0.3304679250
## 168                 -0.1096451720                -0.0329636050
## 169                  0.4720811750                 0.6249039250
## 170                 -0.0232985825                -0.0699599250
## 171                  0.0799114300                 0.0953466500
## 172                 -0.1130805943                -0.0429104750
## 173                 -0.0981153925                -0.0465334050
## 174                 -0.0218595150                 0.0090885297
## 175                 -0.2184452275                -0.1899410500
## 176                 -0.0614028675                -0.0174139200
## 177                  0.0543344750                 0.1363491750
## 178                 -0.2669732575                -0.2345762250
## 179                 -0.2014907900                -0.2540902500
## 180                 -0.0949722975                -0.0417175675
## 181                 -0.0544393087                -0.0466912325
## 182                  0.1679761200                 0.2706039250
## 183                 -0.0461823430                -0.0790041200
## 184                 -0.0137227275                 0.0518772025
## 185                 -0.2031563450                -0.1934954500
## 186                  0.0653574250                 0.1880194500
## 187                 -0.1140116725                 0.0297684050
## 188                  0.0166401283                 0.0409329600
## 189                 -0.4266552750                -0.4016665500
## 190                  0.1491199225                 0.1607533000
## 191                 -0.2616204370                -0.2109528000
## 192                 -0.1013490100                -0.1502052750
## 193                 -0.1259570650                -0.0657479325
## 194                  0.0988663000                 0.2066138000
## 195                  0.1719708250                 0.2686222000
## 196                  0.1899258175                 0.1359323000
## 197                 -0.2201802100                -0.2005081750
## 198                 -0.0848233720                -0.0733176925
## 199                 -0.4260526805                -0.4143595500
## 200                 -0.0955655873                -0.0594820925
## 201                 -0.1054259100                -0.1107120750
## 202                 -0.0402641482                 0.0109840525
## 203                  0.2699267150                 0.3194276250
## 204                  0.0087581500                 0.0921838025
## 205                 -0.3131740950                -0.3292692250
## 206                 -0.1482514400                 0.0137196100
## 207                  0.2489700175                 0.3137639500
## 208                  0.0165134625                 0.0646740650
## 209                  0.0653574250                 0.1880194500
## 210                 -0.4621849900                -0.4785732250
## 211                  0.0337829425                 0.0961642100
## 212                 -0.2423829025                -0.2025060750
## 213                 -0.0162604625                 0.0494421550
## 214                 -0.0825211800                 0.0295165575
## 215                 -0.2507833975                -0.1437615000
## 216                 -0.2392160650                -0.2590690000
## 217                 -0.0088977525                -0.0375267550
## 218                 -0.0402641482                 0.0109840525
## 219                 -0.1042202975                -0.0449024175
## 220                  0.0850187650                 0.1530626750
## 221                  0.1164159250                 0.2323127750
## 222                 -0.0603200700                -0.0307456975
## 223                 -0.1915514950                -0.1224178250
## 224                 -0.2063742700                -0.1428433250
## 225                 -0.1056938670                -0.0501751550
## 226                  0.0777859250                 0.1822754500
## 227                 -0.1233483100                -0.0862648000
## 228                 -0.0058348775                 0.0735266800
## 229                 -0.0517511675                 0.0457927750
## 230                 -0.1135353250                 0.0586507875
## 231                 -0.0623129825                 0.0402560725
## 232                 -0.0634591275                 0.0407736650
## 233                  0.0307805250                 0.0907188600
## 234                 -0.0632760283                -0.0194770000
## 235                 -0.1089608300                -0.0381547125
## 236                 -0.1449189450                -0.0814102600
## 237                  0.0218214250                 0.1034818000
## 238                 -0.0475343200                 0.0716968650
## 239                 -0.4394507475                -0.4092875000
## 240                  0.0344936250                 0.1518030750
## 241                  0.4908571925                 0.5225771000
## 242                 -0.2608920500                -0.1928169000
## 243                 -0.2263662315                -0.1910247000
## 244                 -0.2332066825                -0.1485298000
## 245                 -0.2522117072                -0.2699418000
## 246                  0.0054888625                 0.0918789100
## 247                  0.1826034575                 0.2567951500
## 248                  0.0866361350                 0.0803365625
## 249                 -0.0943227548                -0.0562440475
## 250                  0.1398279975                 0.1615482250
## 251                 -0.3229114750                -0.2494944250
## 252                 -0.2595191525                -0.1473240500
## 253                  0.1132784750                 0.1976310000
## 254                  0.0929225250                 0.2549627250
## 255                 -0.1009324675                -0.0492983250
## 256                 -0.1906947947                -0.1666181250
## 257                 -0.0992285750                -0.0765340875
## 258                  0.0481715000                 0.1578835250
## 259                  0.2304193375                 0.2890260750
## 260                 -0.1257237675                -0.0842190475
## 261                  0.1016963250                 0.2184835000
## 262                  0.0266542550                 0.1181100000
## 263                 -0.1135353250                 0.0586507875
## 264                  0.0873841000                 0.1711718500
## 265                 -0.2138736530                -0.1936598750
## 266                 -0.3202135597                -0.3424044000
## 267                 -0.2012956228                -0.2472916250
## 268                 -0.1213029550                -0.0912862375
## 269                 -0.0488988000                -0.0154826300
## 270                 -0.0125801100                 0.0210811400
## 271                  0.1364257125                 0.2238353250
## 272                 -0.1316199750                -0.0791687250
## 273                  0.1029964225                 0.1645003000
## 274                 -0.2791243975                -0.2437211250
## 275                 -0.2396485375                -0.1556665250
## 276                 -0.3116012770                -0.2613100750
## 277                  0.0234945835                -0.0182877800
## 278                 -0.3312603500                -0.2381038250
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## 688                 -0.1685403763                -0.2343144750
## 689                 -0.0375688560                -0.0714634775
## 690                 -0.2506725250                -0.2656446500
## 691                 -0.2049783125                -0.1873729500
## 692                 -0.4676864000                -0.2965283000
## 693                 -0.1974226275                -0.1730332750
## 694                 -0.0490917323                -0.0042155378
## 695                 -0.3229114750                -0.2494944250
## 696                 -0.1330371300                 0.0137489325
## 697                 -0.3199428325                -0.3467579000
## 698                 -0.1978051550                -0.1354925250
## 699                 -0.0965985509                -0.0681999725
## 700                  0.1136372000                 0.2314950750
## 701                  0.0179406475                 0.0632649050
## 702                 -0.2115336925                -0.2040263250
## 703                  0.0319061525                 0.0143923800
## 704                 -0.2568930387                -0.2348893500
## 705                 -0.1743162575                -0.1409790000
## 706                 -0.2546402725                -0.2075027250
## 707                 -0.2671073000                -0.2357025250
## 708                 -0.2063781400                -0.1501660250
## 709                  0.1071312250                 0.2106460750
## 710                 -0.2742015250                -0.2208239750
## 711                 -0.3148138825                -0.2890800500
## 712                  0.1221819250                 0.2077147000
## 713                 -0.3120654300                -0.3198844750
## 714                 -0.4595995125                -0.4277072500
## 715                 -0.2034222050                -0.1836820000
## 716                 -0.0055883830                 0.0010548435
## 717                  0.0285786000                 0.0766086125
## 718                  0.0056332687                -0.0297878125
## 719                 -0.2092337650                -0.1826809000
## 720                  0.0283241699                -0.0038968663
## 721                 -0.1316543725                -0.0631103400
## 722                  0.0849805425                 0.0901044875
## 723                  0.1816118000                 0.2648733500
## 724                 -0.0945230375                -0.0408211775
## 725                 -0.2185973500                -0.1717729000
## 726                 -0.2994153600                -0.2345292000
## 727                 -0.0371869600                -0.0753461100
## 728                  0.1032227750                 0.2040417750
## 729                 -0.4231644750                -0.3685524750
## 730                  0.2665046200                 0.3304679250
## 731                 -0.0260114000                 0.0509781825
## 732                  0.0431486475                 0.1207803750
## 733                  0.0074469750                 0.1106872000
## 734                 -0.1981436500                -0.2006994750
## 735                  0.1232795900                 0.2326315750
## 736                 -0.2878304525                -0.1668595500
## 737                 -0.0071573325                -0.0720511950
## 738                  0.1089820255                 0.0660061300
## 739                 -0.2732388675                -0.2284782750
## 740                 -0.0861085875                 0.0583085000
## 741                 -0.3529096325                -0.3597181000
## 742                 -0.2103228425                -0.1982695250
## 743                 -0.2075470725                -0.1802864250
## 744                 -0.1259570650                -0.0657479325
## 745                  0.0481715000                 0.1578835250
## 746                  0.0004115142                 0.0032004362
## 747                  0.0151019850                 0.0412134700
## 748                  0.0151019850                 0.0412134700
## 749                 -0.2365441500                -0.1527893750
## 750                 -0.0071573325                -0.0720511950
## 751                 -0.4725332625                -0.4588188750
## 752                 -0.0271201350                 0.0206561400
## 753                  0.1232795900                 0.2326315750
## 754                 -0.2941384775                -0.2190379000
## 755                  0.0231165847                -0.0282713450
## 756                  0.1136372000                 0.2314950750
## 757                 -0.2003080600                -0.1984868750
## 758                  0.0985735500                 0.2167751000
## 759                 -0.1966766100                -0.1870366000
## 760                 -0.0993529300                -0.0742084525
## 761                 -0.0503296112                -0.0172218900
## 762                 -0.2472085300                -0.2575571750
## 763                 -0.1026131500                 0.0419347525
## 764                 -0.2314399188                -0.2475236500
## 765                 -0.1758353750                -0.1445229500
## 766                 -0.3202135597                -0.3424044000
## 767                  0.0653574250                 0.1880194500
## 768                  0.0020782450                 0.0109814160
## 769                 -0.4190778000                -0.2785260750
## 770                 -0.2095276750                -0.1866928500
## 771                 -0.4128788975                -0.3842463750
## 772                 -0.1027247275                -0.0569447250
## 773                 -0.3728243075                -0.3636273750
## 774                 -0.4133638250                -0.2794286000
## 775                  0.0129251750                 0.0795322600
## 776                 -0.0101532083                 0.0062649262
## 777                 -0.1163060775                -0.0627305175
## 778                  0.0296226750                 0.1589313250
## 779                 -0.4214527000                -0.3156096000
## 780                  0.0483084475                 0.0658309075
## 781                 -0.1879599425                -0.1928420250
## 782                 -0.4260526805                -0.4143595500
## 783                  0.0109644200                 0.0437538775
## 784                  0.0348628250                 0.0522356050
## 785                  0.0285786000                 0.0766086125
## 786                 -0.2142361600                -0.1790014250
## 787                 -0.1744305150                -0.1556889250
## 788                 -0.0162604625                 0.0494421550
## 789                  0.4202985500                 0.5087338500
## 790                 -0.1806364675                -0.1660885000
## 791                 -0.3828973925                -0.3859260500
## 792                 -0.2563942550                -0.2580483750
## 793                 -0.1871489125                -0.1465015500
## 794                  0.0773101775                 0.1571741750
## 795                 -0.2435570975                -0.1594991750
## 796                 -0.4463306950                -0.4344721500
## 797                  0.0850187650                 0.1530626750
## 798                  0.1341453000                 0.2457646750
## 799                 -0.2092337650                -0.1826809000
## 800                  0.0348054850                 0.0571703425
## 801                 -0.1330371300                 0.0137489325
## 802                 -0.2090304100                -0.1791578750
## 803                 -0.2151241400                -0.1903565000
## 804                  0.0828690750                 0.1583681250
## 805                 -0.2440406475                -0.2281029250
## 806                 -0.2002939975                -0.1910359500
## 807                  0.0011759000                 0.1173880250
## 808                 -0.5003928500                -0.3454779500
## 809                 -0.0509505528                -0.0757518675
## 810                 -0.3116012770                -0.2613100750
## 811                 -0.2233579275                -0.1800144250
## 812                  0.0032417050                 0.0182428000
## 813                 -0.2355535575                -0.2138766000
##     upper.975_q_clay_skill_loser upper.975_q_grass_skill_loser
## 1                    0.688993974                   0.665278396
## 2                    0.953349700                   0.606928907
## 3                    0.771674895                   0.693746298
## 4                    0.186850517                   0.270680550
## 5                    0.421111050                   0.352777540
## 6                    0.073433792                   0.153825497
## 7                    0.765897037                   0.624367285
## 8                    0.388323750                   0.264573193
## 9                    0.268395020                   0.231453970
## 10                   0.590564545                   0.628872770
## 11                   0.982041350                   0.594240515
## 12                   0.436541350                   0.392590612
## 13                   0.320694205                   0.352161955
## 14                   0.966322325                   0.590372995
## 15                   0.327393475                   0.330992007
## 16                   0.599228457                   0.657296805
## 17                   0.984964100                   0.574502965
## 18                   0.662905900                   0.439199037
## 19                   0.761892125                   0.659867893
## 20                   0.248538960                   0.259876460
## 21                   0.374615130                   0.232241662
## 22                   0.400637982                   0.395902107
## 23                   0.392224385                   0.380294730
## 24                   0.244801160                   0.252538625
## 25                   0.269685102                   0.297272097
## 26                   0.186157419                   0.127186787
## 27                   0.105059125                   0.038290805
## 28                   0.974472275                   0.590253681
## 29                   0.327393475                   0.330992007
## 30                   0.387073977                   0.348948230
## 31                   0.297422127                   0.266098775
## 32                   0.230939837                   0.212403880
## 33                   0.281241332                   0.309190835
## 34                   0.331306335                   0.346896652
## 35                   0.371093175                   0.278503785
## 36                   0.426737220                   0.364523415
## 37                   0.388453590                   0.383501935
## 38                   0.310776905                   0.251104600
## 39                   0.108217975                  -0.012278583
## 40                   0.004558162                   0.233700137
## 41                   0.392886650                   0.365742377
## 42                   0.267454653                   0.251516792
## 43                   0.395997400                   0.271592267
## 44                   0.454871302                   0.496971932
## 45                   0.603135905                   0.656954965
## 46                   0.676830765                   0.652317305
## 47                   0.951663775                   0.575151647
## 48                   0.410336025                   0.217822440
## 49                   0.290557785                   0.303168557
## 50                   0.403923107                   0.381231360
## 51                   0.421048777                   0.388045492
## 52                   0.221774970                   0.190588510
## 53                   0.223297930                   0.344261840
## 54                   0.311101300                   0.240293232
## 55                   0.253001827                   0.163960697
## 56                   0.774990247                   0.641580590
## 57                   0.667449900                   0.462925920
## 58                   0.413420867                   0.397920332
## 59                   0.328155645                   0.442224725
## 60                   0.239165677                   0.360183325
## 61                   0.277407947                   0.309877690
## 62                   0.330701975                   0.317525593
## 63                   0.498075455                   0.473022727
## 64                   0.246100801                   0.252515445
## 65                   0.422947507                   0.463001657
## 66                   0.387606850                   0.349482513
## 67                   0.301792630                   0.291849255
## 68                   0.338073100                   0.442305250
## 69                   0.151441690                   0.132240447
## 70                   0.419646827                   0.375226535
## 71                   0.254766802                   0.272381940
## 72                   0.390011187                   0.403407945
## 73                   0.323784635                   0.294582315
## 74                   0.423378155                   0.394784095
## 75                   0.252234335                   0.257664800
## 76                   0.128898207                   0.059445482
## 77                   0.667650925                   0.459031300
## 78                   0.219119235                   0.155565225
## 79                   0.427099520                   0.462227990
## 80                   0.285460995                   0.314189960
## 81                   0.424823575                   0.256037730
## 82                   0.078471977                   0.249139857
## 83                   0.248538960                   0.259876460
## 84                   0.208854952                   0.140322727
## 85                   0.438108250                   0.349575481
## 86                   0.344974137                   0.356464475
## 87                   0.267435897                   0.324854358
## 88                   0.276026249                   0.259519660
## 89                   0.245781070                   0.247798332
## 90                   0.098426425                   0.034809560
## 91                   0.087366300                  -0.012100758
## 92                   0.323472632                   0.335845300
## 93                   0.758271257                   0.686528090
## 94                   0.283946105                   0.301153350
## 95                   0.755858743                   0.681438187
## 96                   0.468329597                   0.459999257
## 97                  -0.045095653                   0.088729415
## 98                   0.378752000                   0.447484210
## 99                   0.501020800                   0.481054782
## 100                  0.019076492                   0.195364442
## 101                  0.357696025                   0.278376560
## 102                  0.425490085                   0.358720670
## 103                  0.655067900                   0.477346452
## 104                  0.522315575                   0.465430045
## 105                  0.348392125                   0.191946903
## 106                  0.231813882                   0.215878902
## 107                  0.764515895                   0.649894665
## 108                  0.342167612                   0.188407075
## 109                  0.347150148                   0.183705525
## 110                  0.152371710                  -0.078243108
## 111                  0.388085156                   0.391050485
## 112                  0.235984371                   0.103568455
## 113                  0.081555887                   0.280503127
## 114                  0.312443800                   0.323284367
## 115                  0.267058625                   0.290273190
## 116                  0.244425382                   0.173568060
## 117                  0.264444142                   0.255910680
## 118                  0.260053775                   0.192452605
## 119                  0.759190052                   0.662463820
## 120                  0.220947027                   0.208757205
## 121                  0.335751100                   0.170704360
## 122                  0.305169105                   0.169954805
## 123                  0.393918375                   0.338738840
## 124                  0.230939837                   0.212403880
## 125                  0.291375100                   0.294917730
## 126                  0.315150145                   0.242161245
## 127                  0.371093175                   0.278503785
## 128                  0.281719962                   0.334716870
## 129                  0.186157419                   0.127186787
## 130                  0.405797067                   0.386999272
## 131                 -0.044860455                   0.050269507
## 132                  0.298263367                   0.269583785
## 133                  0.061693102                   0.076774579
## 134                  0.958860750                   0.561929295
## 135                  0.348955725                   0.198883644
## 136                  0.450520050                   0.362932857
## 137                  0.081279812                   0.174026477
## 138                  0.398212130                   0.435830425
## 139                  0.392886650                   0.365742377
## 140                  0.079714485                   0.171022900
## 141                  0.257944605                   0.282265550
## 142                  0.297422127                   0.266098775
## 143                  0.309456411                   0.337777366
## 144                  0.170126962                   0.122125552
## 145                  0.424363295                   0.416122210
## 146                  0.276197600                   0.146849252
## 147                  0.331167500                   0.317718862
## 148                 -0.002856145                   0.074861787
## 149                  0.019076492                   0.195364442
## 150                  0.425490085                   0.358720670
## 151                  0.177533167                   0.084446067
## 152                  0.256757390                   0.261903710
## 153                  0.239985425                   0.175460715
## 154                  0.323472632                   0.335845300
## 155                  0.225226632                   0.336001467
## 156                  0.178779537                   0.095725410
## 157                  0.103753025                   0.038019156
## 158                  0.347150148                   0.183705525
## 159                  0.286545175                   0.341400410
## 160                  0.221103165                   0.150776655
## 161                  0.115889497                   0.183648243
## 162                  0.186016352                   0.211709407
## 163                  0.267624056                   0.226861857
## 164                 -0.014693998                  -0.010632690
## 165                  0.271575412                   0.249899777
## 166                  0.302475247                   0.332786475
## 167                  0.505404075                   0.470407815
## 168                  0.231451256                   0.154889832
## 169                  0.759505827                   0.674940830
## 170                 -0.026907918                   0.248290420
## 171                  0.176111560                   0.340341750
## 172                  0.315150145                   0.242161245
## 173                  0.177495847                   0.191788367
## 174                  0.372451100                   0.210950667
## 175                 -0.042726144                   0.059353835
## 176                  0.110490545                   0.190094667
## 177                  0.395997400                   0.271592267
## 178                  0.112961675                   0.015318310
## 179                  0.001464257                   0.115831280
## 180                  0.222282885                   0.149408285
## 181                  0.107889407                   0.191846957
## 182                  0.408910545                   0.389220207
## 183                  0.071898272                   0.218599400
## 184                  0.265757912                   0.264245445
## 185                  0.110054900                   0.056335697
## 186                  0.316962710                   0.300407408
## 187                  0.323107400                   0.177009832
## 188                  0.246141577                   0.265559877
## 189                  0.051795285                   0.061140105
## 190                  0.225847680                   0.346290015
## 191                  0.224324910                   0.123317625
## 192                  0.196354505                   0.247526997
## 193                  0.088821462                   0.171370682
## 194                  0.393918375                   0.338738840
## 195                  0.404693435                   0.392155065
## 196                  0.331895350                   0.412653275
## 197                 -0.052974672                   0.063662617
## 198                  0.118125086                   0.177787900
## 199                  0.034744315                   0.056719575
## 200                  0.253558025                   0.202557502
## 201                  0.112536562                   0.190655385
## 202                  0.225417267                   0.204573490
## 203                  0.420800587                   0.465157542
## 204                  0.270558012                   0.266021503
## 205                 -0.004695425                   0.073742125
## 206                  0.323874892                   0.169259262
## 207                  0.530108625                   0.476497060
## 208                  0.134910283                   0.258461640
## 209                  0.316962710                   0.300407408
## 210                  0.055445680                   0.034127895
## 211                  0.370144275                   0.279252355
## 212                  0.208854952                   0.140322727
## 213                  0.248540687                   0.260794727
## 214                  0.323493995                   0.253268277
## 215                  0.250888107                   0.071465120
## 216                 -0.008417460                   0.055689695
## 217                  0.101168625                   0.257813515
## 218                  0.225417267                   0.204573490
## 219                  0.327319802                   0.224025215
## 220                  0.275110667                   0.288301950
## 221                  0.450520050                   0.362932857
## 222                  0.128829332                   0.193237875
## 223                  0.080414727                   0.101455404
## 224                  0.249349507                   0.195272412
## 225                  0.231857027                   0.172216478
## 226                  0.314537750                   0.293841275
## 227                  0.250841620                   0.191390575
## 228                  0.330748842                   0.289619475
## 229                  0.166569352                   0.242138592
## 230                  0.343347930                   0.187450413
## 231                  0.266543900                   0.196741507
## 232                  0.264905500                   0.212270250
## 233                  0.383140350                   0.268512450
## 234                  0.209963012                   0.186310047
## 235                  0.268381500                   0.171942276
## 236                  0.214549953                   0.179023059
## 237                  0.432244225                   0.258096782
## 238                  0.410336025                   0.217822440
## 239                  0.060091097                   0.085802232
## 240                  0.271559840                   0.305540993
## 241                  0.560964045                   0.674110222
## 242                  0.217932279                   0.047807485
## 243                  0.200702532                   0.128976662
## 244                  0.207750722                   0.105642877
## 245                  0.054927505                   0.102898305
## 246                  0.231813882                   0.215878902
## 247                  0.424363295                   0.416122210
## 248                  0.147041840                   0.322803025
## 249                  0.263529084                   0.217116397
## 250                  0.228165325                   0.347923510
## 251                  0.094356510                  -0.014218735
## 252                  0.205985355                   0.100379660
## 253                  0.277243977                   0.361895850
## 254                  0.466723775                   0.330983500
## 255                  0.367157300                   0.237644500
## 256                  0.115875525                   0.060616645
## 257                  0.236922827                   0.190805095
## 258                  0.277657340                   0.303543692
## 259                  0.420566495                   0.454516170
## 260                  0.330320832                   0.224393470
## 261                  0.359334705                   0.350000967
## 262                  0.424823575                   0.256037730
## 263                  0.343347930                   0.187450413
## 264                  0.281241332                   0.309190835
## 265                  0.126647540                   0.076906955
## 266                 -0.014993838                   0.077977040
## 267                 -0.009367858                   0.104970072
## 268                  0.232915517                   0.192795100
## 269                  0.214451250                   0.181778502
## 270                  0.296277190                   0.369160665
## 271                  0.395714165                   0.389115555
## 272                  0.297272197                   0.171170840
## 273                  0.265993020                   0.313638070
## 274                  0.105413722                   0.013577882
## 275                  0.310103790                   0.145921987
## 276                  0.146722640                   0.115050160
## 277                  0.065979473                   0.298751825
## 278                  0.176126375                   0.098708145
## 279                  0.313221244                   0.299283747
## 280                  0.246970700                   0.148098392
## 281                  0.168519265                   0.337562975
## 282                  0.006793760                   0.202781926
## 283                 -0.043681330                   0.111345046
## 284                  0.193778095                   0.060906505
## 285                  0.164188287                   0.150549810
## 286                  0.182197485                   0.255637630
## 287                  0.106289917                  -0.009787705
## 288                  0.173390812                   0.143298722
## 289                  0.146232735                   0.083101105
## 290                  0.098553307                   0.276442665
## 291                  0.468329597                   0.459999257
## 292                  0.230192232                   0.253135802
## 293                  0.357696025                   0.278376560
## 294                  0.053429307                   0.263844942
## 295                  0.141017518                   0.149618932
## 296                  0.291133857                   0.344958462
## 297                 -0.062917673                   0.059176385
## 298                  0.118920070                   0.246873750
## 299                  0.118920070                   0.246873750
## 300                  0.109076235                   0.047939430
## 301                  0.216492000                   0.186660207
## 302                 -0.051853268                   0.064091787
## 303                  0.056283855                   0.298122550
## 304                  0.110163786                   0.236089705
## 305                 -0.045478085                   0.063832630
## 306                 -0.062917673                   0.059176385
## 307                  0.313055290                   0.337909555
## 308                  0.150165535                   0.059423405
## 309                  0.179394072                   0.087830911
## 310                  0.163457747                   0.191159992
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## 635                 0.2151224750
## 636                 0.2485927250
## 637                 0.2819706750
## 638                -0.0033960193
## 639                 0.0016769827
## 640                 0.1493363000
## 641                 0.1447128250
## 642                 0.1083042000
## 643                 0.1701444000
## 644                 0.1739466000
## 645                -0.0518422400
## 646                -0.0660532475
## 647                 0.2048046000
## 648                 0.3784460250
## 649                 0.4119462750
## 650                -0.0432790200
## 651                 0.1054362750
## 652                 0.0155508875
## 653                 0.2237472000
## 654                 0.0224886150
## 655                 0.2823118500
## 656                 0.2268008750
## 657                -0.0208449700
## 658                -0.0299724725
## 659                 0.1923891750
## 660                 0.2958899250
## 661                 0.0408551825
## 662                 0.0301779300
## 663                 0.0572553575
## 664                 0.3805248250
## 665                 0.2377099250
## 666                -0.0399083050
## 667                -0.0627802575
## 668                 0.1402699000
## 669                 0.2096113250
## 670                 0.0065123010
## 671                -0.0400493800
## 672                 0.0432857500
## 673                -0.0128357250
## 674                -0.0602949175
## 675                 0.2453308750
## 676                 0.0135272025
## 677                 0.1836819750
## 678                 0.3772041000
## 679                 0.1147559250
## 680                 0.1316652500
## 681                 0.2029344750
## 682                 0.0936695000
## 683                 0.1271339250
## 684                -0.0494797775
## 685                 0.0230111450
## 686                 0.4997931250
## 687                 0.0546993075
## 688                -0.0214336475
## 689                 0.0959202725
## 690                -0.0390408000
## 691                 0.0347889900
## 692                -0.0900817075
## 693                 0.0103087625
## 694                 0.1735770500
## 695                -0.0527592450
## 696                 0.1739466000
## 697                -0.0447220525
## 698                 0.0575644525
## 699                 0.1142768000
## 700                 0.3658792250
## 701                 0.2190184750
## 702                 0.0243834750
## 703                 0.1843013000
## 704                -0.0386064025
## 705                 0.1058119500
## 706                 0.0478108350
## 707                -0.0427788700
## 708                 0.1104466750
## 709                 0.3426002250
## 710                 0.0233612850
## 711                 0.1126469500
## 712                 0.3685929250
## 713                -0.0669945975
## 714                 0.0148898550
## 715                 0.0378151525
## 716                 0.1877827500
## 717                 0.2203409250
## 718                 0.1557009000
## 719                 0.0168304175
## 720                 0.1520866750
## 721                 0.1392636250
## 722                 0.2345307000
## 723                 0.3930374750
## 724                 0.1450103750
## 725                 0.0486795225
## 726                 0.0301779300
## 727                 0.0999362000
## 728                 0.3602374000
## 729                -0.0404301075
## 730                 0.4526618500
## 731                 0.2243795250
## 732                 0.2551916250
## 733                 0.2567217750
## 734                 0.0082189495
## 735                 0.3708462750
## 736                 0.1154278750
## 737                 0.1049498000
## 738                 0.2220123500
## 739                 0.0685101125
## 740                 0.2298009750
## 741                -0.0632076550
## 742                 0.0242478875
## 743                 0.0360377650
## 744                 0.1198624250
## 745                 0.2874575750
## 746                 0.2087202250
## 747                 0.2244040250
## 748                 0.2244040250
## 749                 0.0919827650
## 750                 0.1049498000
## 751                -0.1591980500
## 752                 0.1698047250
## 753                 0.3708462750
## 754                 0.0304710250
## 755                 0.1773992000
## 756                 0.3658792250
## 757                 0.0325124800
## 758                 0.3550633750
## 759                -0.0086741903
## 760                 0.1427716750
## 761                 0.2082981750
## 762                -0.0190317200
## 763                 0.2235115000
## 764                 0.0329411300
## 765                 0.0224886150
## 766                -0.0156747025
## 767                 0.3168163000
## 768                 0.2020570250
## 769                -0.0627802575
## 770                 0.0050455120
## 771                 0.0066382510
## 772                 0.2509988250
## 773                 0.0964801200
## 774                -0.0602949175
## 775                 0.2457897500
## 776                 0.2111622000
## 777                 0.2326650500
## 778                 0.2926743500
## 779                -0.0523886650
## 780                 0.2048046000
## 781                 0.0394088000
## 782                 0.0016769827
## 783                 0.2296266000
## 784                 0.2058085250
## 785                 0.2203409250
## 786                 0.0964035025
## 787                 0.0187015525
## 788                 0.2275434000
## 789                 0.6508987000
## 790                 0.3830418500
## 791                 0.0047564495
## 792                -0.0200982750
## 793                 0.0427154800
## 794                 0.2779425250
## 795                 0.0730015475
## 796                -0.0076872353
## 797                 0.2732163750
## 798                 0.3812856250
## 799                 0.0168304175
## 800                 0.2055832250
## 801                 0.1739466000
## 802                 0.1367528000
## 803                 0.0040324590
## 804                 0.2754429750
## 805                -0.0323322225
## 806                -0.0146652275
## 807                 0.2717999500
## 808                -0.0714233550
## 809                 0.0816199975
## 810                 0.0581643000
## 811                 0.0631453100
## 812                 0.1547532750
## 813                 0.0817595550
multi_t_games_model_bets %>%
  filter(best_odds_profit > 0) %>%
  arrange(desc(best_odds_profit))
##    winner_id loser_id                    score set_order winner_y  n winner_age
## 1     104660   103819 6-7(5) 7-6(5) 7-5 7-6(5)      0111       27 51   27.46338
## 2     104327   104745        7-6(4) 7-6(8) 6-4       111       20 36   29.28131
## 3     105023   104925    7-6(6) 6-1 3-6 7-6(5)      1101       23 42   28.72279
## 4     103163   103819           2-6 7-6(8) 6-4       011       15 31   39.19233
## 5     103781   106233                  6-3 7-5        11       13 21   35.15674
## 6     103970   104755          6-3 6-4 5-7 6-2      1101       23 39   35.25257
## 7     103888   104678                  6-2 6-2        11       12 16   33.68652
## 8     104269   100644          6-4 3-6 6-4 6-2      1011       21 37   33.53593
## 9     104918   105683        6-4 7-6(3) 7-6(2)       111       20 36   29.11978
## 10    103163   105332                  6-2 6-3        11       12 17   39.03901
##    loser_age N_months_since_last_match_winner N_months_since_last_match_loser
## 1   31.87680                                0                               0
## 2   27.05818                                0                               0
## 3   29.10062                                0                               0
## 4   35.84394                                0                               2
## 5   22.87201                                0                               0
## 6   31.04175                                0                               0
## 7   29.51403                                0                               0
## 8   20.10678                                0                               0
## 9   25.50034                                0                               0
## 10  27.94251                                0                               0
##    surface tourney_date      month winner_rank loser_rank pp_p1_set_win_prob
## 1        3   2013-06-24 2013-06-01         116          3          0.1963428
## 2        3   2013-06-24 2013-06-01         135          5          0.2316756
## 3        3   2016-06-27 2016-06-01          41          1          0.2376445
## 4        3   2017-06-12 2017-06-01         302          5          0.3289500
## 5        2   2016-07-18 2016-07-01         421          9          0.3836712
## 6        3   2017-07-03 2017-07-01          39         27          0.5006097
## 7        1   2015-08-16 2015-08-01        1034         20          0.6092496
## 8        2   2017-05-29 2017-05-01          37         10          0.6242121
## 9        3   2016-06-27 2016-06-01           2          7          0.6825169
## 10       2   2017-04-17 2017-04-01         655         40          0.6537740
##    pp_p1_match_win_prob pp_p1_y             model year  full_name_winner
## 1            0.05876177      25 Multi-T_bin_games 2013 Sergiy Stakhovsky
## 2            0.09124023      26 Multi-T_bin_games 2013      Steve Darcis
## 3            0.09349758      26 Multi-T_bin_games 2016       Sam Querrey
## 4            0.25493412      17 Multi-T_bin_games 2017        Tommy Haas
## 5            0.32962258      18 Multi-T_bin_games 2016     Jurgen Melzer
## 6            0.50116288      32 Multi-T_bin_games 2017      David Ferrer
## 7            0.66074755      21 Multi-T_bin_games 2015        Mardy Fish
## 8            0.72037897      35 Multi-T_bin_games 2017 Fernando Verdasco
## 9            0.81006598      37 Multi-T_bin_games 2016       Andy Murray
## 10           0.72193069      22 Multi-T_bin_games 2017        Tommy Haas
##     full_name_loser          score2  MaxW MaxL  AvgW AvgL
## 1     Roger Federer 6-7 7-6 7-5 7-6 61.00 1.01 22.96 1.01
## 2      Rafael Nadal     7-6 7-6 6-4 46.00 1.02 20.68 1.01
## 3    Novak Djokovic 7-6 6-1 3-6 7-6 39.75 1.02 20.78 1.01
## 4     Roger Federer     2-6 7-6 6-4 11.88 1.08  8.92 1.06
## 5     Dominic Thiem         6-3 7-5  9.50 1.11  7.98 1.07
## 6   Richard Gasquet 6-3 6-4 5-7 6-2  8.50 1.15  6.65 1.11
## 7    Viktor Troicki         6-2 6-2  5.75 1.20  5.08 1.16
## 8  Alexander Zverev 6-4 3-6 6-4 6-2  5.38 1.20  4.92 1.17
## 9      Milos Raonic     6-4 7-6 7-6  4.36 1.30  3.97 1.26
## 10     Benoit Paire         6-2 6-3  4.05 1.29  3.86 1.25
##    best_winner_exp_payout best_loser_exp_payout avg_winner_exp_payout
## 1                2.584468           -0.04934938             0.3491702
## 2                3.197051           -0.07306503             0.8868480
## 3                2.716529           -0.07536753             0.9428797
## 4                2.028617           -0.19532885             1.2740124
## 5                2.131415           -0.25588107             1.6303882
## 6                3.259884           -0.42633731             2.3327332
## 7                2.799298           -0.59289707             2.3565976
## 8                2.875639           -0.66445476             2.5442645
## 9                2.531888           -0.75308578             2.2159619
## 10               1.923819           -0.64129059             1.7866525
##    avg_loser_exp_payout max_exp_payout avg_exp_payout best_odds_profit
## 1           -0.04934938       2.584468      0.3491702            60.00
## 2           -0.08215263       3.197051      0.8868480            45.00
## 3           -0.08443256       2.716529      0.9428797            38.75
## 4           -0.21023017       2.028617      1.2740124            10.88
## 5           -0.28269616       2.131415      1.6303882             8.50
## 6           -0.44629080       3.259884      2.3327332             7.50
## 7           -0.60646716       2.799298      2.3565976             4.75
## 8           -0.67284339       2.875639      2.5442645             4.38
## 9           -0.76068314       2.531888      2.2159619             3.36
## 10          -0.65241336       1.923819      1.7866525             3.05
##    full_name_winner_winner posterior_mean_clay_skill_winner
## 1        Sergiy Stakhovsky                      -0.09224965
## 2             Steve Darcis                      -0.05020994
## 3              Sam Querrey                       0.11470588
## 4               Tommy Haas                       0.29183059
## 5            Jurgen Melzer                       0.10877617
## 6             David Ferrer                       0.53687299
## 7               Mardy Fish                       0.18673365
## 8        Fernando Verdasco                       0.33042933
## 9              Andy Murray                       0.54257312
## 10              Tommy Haas                       0.32669530
##    posterior_mean_grass_skill_winner posterior_mean_hard_skill_winner
## 1                         0.07527216                       0.04494766
## 2                         0.04085384                       0.01891567
## 3                         0.20641211                       0.19285869
## 4                         0.24895066                       0.23741133
## 5                         0.12945522                       0.13044653
## 6                         0.31236917                       0.39032879
## 7                         0.34447092                       0.33229409
## 8                         0.18923188                       0.25139282
## 9                         0.54950617                       0.56365883
## 10                        0.24686416                       0.24005553
##    posterior_sd_clay_skill_winner posterior_sd_grass_skill_winner
## 1                      0.05576709                      0.05876358
## 2                      0.06540644                      0.06224883
## 3                      0.04420291                      0.03776888
## 4                      0.04742965                      0.04892136
## 5                      0.03853420                      0.04348034
## 6                      0.02935726                      0.04547992
## 7                      0.06223958                      0.05272650
## 8                      0.03254707                      0.04133618
## 9                      0.04060536                      0.04102381
## 10                     0.05227065                      0.05263129
##    posterior_sd_hard_skill_winner posterior_median_clay_skill_winner
## 1                      0.03687901                        -0.09163850
## 2                      0.04964769                        -0.05003597
## 3                      0.02607126                         0.11454225
## 4                      0.03140865                         0.29097355
## 5                      0.02933573                         0.10842349
## 6                      0.02323211                         0.53658100
## 7                      0.03452718                         0.18544000
## 8                      0.02557479                         0.33037140
## 9                      0.02387127                         0.54184060
## 10                     0.03198589                         0.32652825
##    posterior_median_grass_skill_winner posterior_median_hard_skill_winner
## 1                           0.07459905                         0.04441410
## 2                           0.03974190                         0.01840215
## 3                           0.20546075                         0.19248900
## 4                           0.24723133                         0.23731050
## 5                           0.12839951                         0.12904100
## 6                           0.31218640                         0.39027850
## 7                           0.34321795                         0.33086800
## 8                           0.19022770                         0.25214050
## 9                           0.54806185                         0.56350500
## 10                          0.24525863                         0.24020450
##    lower.025_q_clay_skill_winner lower.025_q_grass_skill_winner
## 1                    -0.20316267                    -0.04020534
## 2                    -0.17366034                    -0.07823072
## 3                     0.02892250                     0.13745054
## 4                     0.19952352                     0.15559988
## 5                     0.03601524                     0.05092447
## 6                     0.48157390                     0.22176827
## 7                     0.06901550                     0.24271103
## 8                     0.26950080                     0.10772180
## 9                     0.46328412                     0.47197314
## 10                    0.22697212                     0.14716058
##    lower.025_q_hard_skill_winner upper.975_q_clay_skill_winner
## 1                    -0.02808499                    0.01330298
## 2                    -0.07765175                    0.07627192
## 3                     0.14278633                    0.20041498
## 4                     0.17624513                    0.38578992
## 5                     0.07640066                    0.18364938
## 6                     0.34301087                    0.59344837
## 7                     0.26805455                    0.30787083
## 8                     0.20112555                    0.39568152
## 9                     0.51905380                    0.62404888
## 10                    0.17451995                    0.42722923
##    upper.975_q_grass_skill_winner upper.975_q_hard_skill_winner
## 1                       0.1926295                     0.1155232
## 2                       0.1693405                     0.1184587
## 3                       0.2850858                     0.2447351
## 4                       0.3487652                     0.2971484
## 5                       0.2152060                     0.1894577
## 6                       0.4057635                     0.4348574
## 7                       0.4509536                     0.4060496
## 8                       0.2676507                     0.3017220
## 9                       0.6331927                     0.6111508
## 10                      0.3579434                     0.3002149
##    full_name_loser_loser posterior_mean_clay_skill_loser
## 1          Roger Federer                       0.5782374
## 2           Rafael Nadal                       0.8923698
## 3         Novak Djokovic                       0.7241137
## 4          Roger Federer                       0.5445195
## 5          Dominic Thiem                       0.2765454
## 6        Richard Gasquet                       0.3719237
## 7         Viktor Troicki                       0.1451733
## 8       Alexander Zverev                       0.1506105
## 9           Milos Raonic                       0.3279963
## 10          Benoit Paire                       0.1020373
##    posterior_mean_grass_skill_loser posterior_mean_hard_skill_loser
## 1                        0.56405986                      0.63741614
## 2                        0.46116102                      0.56395278
## 3                        0.61247074                      0.72999289
## 4                        0.55743155                      0.62409204
## 5                        0.10979862                      0.14645616
## 6                        0.31151408                      0.31031221
## 7                        0.15525265                      0.17536899
## 8                        0.20336200                      0.20161320
## 9                        0.27995515                      0.32331856
## 10                       0.03834292                      0.05602189
##    posterior_sd_clay_skill_loser posterior_sd_grass_skill_loser
## 1                     0.04636647                     0.04963280
## 2                     0.04393686                     0.06461534
## 3                     0.03681982                     0.04407514
## 4                     0.03863745                     0.03970180
## 5                     0.04440012                     0.05750566
## 6                     0.03971519                     0.04486434
## 7                     0.03983898                     0.04179865
## 8                     0.05711646                     0.05639121
## 9                     0.04556631                     0.04507652
## 10                    0.04028813                     0.04920456
##    posterior_sd_hard_skill_loser posterior_median_clay_skill_loser
## 1                     0.03068106                         0.5771920
## 2                     0.03466660                         0.8924285
## 3                     0.02378226                         0.7247434
## 4                     0.02401464                         0.5453214
## 5                     0.04115824                         0.2747548
## 6                     0.02447069                         0.3729132
## 7                     0.02823946                         0.1449649
## 8                     0.04106213                         0.1483530
## 9                     0.02565834                         0.3274242
## 10                    0.02991182                         0.1023330
##    posterior_median_grass_skill_loser posterior_median_hard_skill_loser
## 1                          0.56462495                        0.63830550
## 2                          0.45970280                        0.56559350
## 3                          0.61211750                        0.72983200
## 4                          0.55659890                        0.62426050
## 5                          0.11183735                        0.14691900
## 6                          0.30998943                        0.31044550
## 7                          0.15610565                        0.17596000
## 8                          0.20426339                        0.20153950
## 9                          0.28109480                        0.32287450
## 10                         0.03917646                        0.05584285
##    lower.025_q_clay_skill_loser lower.025_q_grass_skill_loser
## 1                    0.48771863                   0.467068525
## 2                    0.80799510                   0.336212600
## 3                    0.65252335                   0.522193975
## 4                    0.46926015                   0.479590150
## 5                    0.18910920                  -0.002281075
## 6                    0.29532113                   0.228371903
## 7                    0.06445698                   0.072560495
## 8                    0.04094787                   0.094033835
## 9                    0.24023863                   0.194324900
## 10                   0.02517968                  -0.059975723
##    lower.025_q_hard_skill_loser upper.975_q_clay_skill_loser
## 1                   0.578039800                    0.6731985
## 2                   0.496037850                    0.9753649
## 3                   0.685672575                    0.7954394
## 4                   0.577255600                    0.6209378
## 5                   0.065779010                    0.3648839
## 6                   0.262316725                    0.4516356
## 7                   0.119675675                    0.2229803
## 8                   0.119113600                    0.2626508
## 9                   0.274831975                    0.4176238
## 10                 -0.001091323                    0.1804437
##    upper.975_q_grass_skill_loser upper.975_q_hard_skill_loser
## 1                      0.6602861                    0.6968319
## 2                      0.5943746                    0.6258220
## 3                      0.6953446                    0.7796431
## 4                      0.6370795                    0.6715561
## 5                      0.2204306                    0.2239004
## 6                      0.4026846                    0.3581013
## 7                      0.2390124                    0.2310133
## 8                      0.3147434                    0.2825368
## 9                      0.3688699                    0.3743003
## 10                     0.1349466                    0.1168410

What if we try a Kelly strategy?

# Fraction for kelly bet
alpha = .25

multi_norm_games_odds = test_out_odds %>%
  filter(model == "Multi-Norm_bin_games")

# Containers
bankroll = rep(0, nrow(multi_norm_games_odds)+1)
bankroll[1] = 100000 # start at 10,000 dollars
wins_losses = rep(0, nrow(multi_norm_games_odds))

for (i in 1:nrow(multi_norm_games_odds)) {
  p1 = multi_norm_games_odds[i, "pp_p1_match_win_prob"]
  b1 = multi_norm_games_odds[i, "MaxW"] - 1
  p2 = 1 - p1
  b2 = multi_norm_games_odds[i, "MaxL"] - 1
  kelly_f_p1 = (p1 - p2 / b1) * alpha
  kelly_f_p2 = (p2 - p1 / b2) * alpha
  max_kelly_f = max(kelly_f_p1, kelly_f_p2)
  # print(kelly_f_p1)
  # print(kelly_f_p2)
  # print(max_kelly_f)
  if (max_kelly_f > 0 & max_kelly_f == kelly_f_p1) {
    wins_losses[i] = 1
    gain = max_kelly_f * bankroll[i] * b1
  } else if (max_kelly_f > 0 & max_kelly_f == kelly_f_p2) {
    wins_losses[i] = -1
    gain = -max_kelly_f * bankroll[i]
  } else {
    wins_losses[i] = 0
    gain = 0
  }
  bankroll[i+1] = bankroll[i] + gain
}

plot(1:length(bankroll), bankroll, type = 'l')

prop.table(table(wins_losses))
## wins_losses
##         -1          0          1 
## 0.55600758 0.02209441 0.42189802

Let’s mess with Kelly criterion later…

We can also plot player skills over time:

players_to_plot = c("Novak Djokovic", "Roger Federer", "Rafael Nadal", "Andy Murray", "Juan Martin del Potro", "David Ferrer", "Tomas Berdych", "Jo-Wilfried Tsonga", "Stan Wawrinka",
                    "Marin Cilic")

ggplot(posterior_mean_frames %>% filter(skill_type == 'hard_skill', model == "Multi-T_bin_games", full_name %in% players_to_plot), 
       aes(month, posterior_mean, color=full_name)) +
  geom_line(linewidth=1.0) +
  #geom_line(aes(month, lower.025_q, color=full_name), linetype='dashed') +
  #geom_line(aes(month, upper.975_q, color=full_name), linetype = 'dashed')  +
  ggtitle("Hard Court Skills") +
  labs(y = 'posterior mean', color = "name")

ggsave("../manuscript/first_draft/images/hard_skills_over_time.png")  
## Saving 7 x 5 in image
ggplot(posterior_mean_frames %>% filter(skill_type == 'clay_skill', model == "Multi-T_bin_games", full_name %in% players_to_plot), 
       aes(month, posterior_mean, color=full_name)) +
  geom_line(linewidth=1.0)  +
  #geom_line(aes(month, lower.025_q, color=full_name), linetype='dashed') +
  #geom_line(aes(month, upper.975_q, color=full_name), linetype = 'dashed')  +
  ggtitle("Clay Court Skills") +
  labs(y = 'posterior mean', color = "name")

ggsave("../manuscript/first_draft/images/clay_skills_over_time.png")  
## Saving 7 x 5 in image
ggplot(posterior_mean_frames %>% filter(skill_type == 'grass_skill', model == "Multi-T_bin_games", full_name %in% players_to_plot), 
       aes(month, posterior_mean, color=full_name)) +
  geom_line(linewidth=1.0)  +
  #geom_line(aes(month, lower.025_q, color=full_name), linetype='dashed') +
  #geom_line(aes(month, upper.975_q, color=full_name), linetype = 'dashed')  +
  ggtitle("Grass Court Skills") +
  labs(y = 'posterior mean', color = "name")

ggsave("../manuscript/first_draft/images/grass_skills_over_time.png")  
## Saving 7 x 5 in image
ggplot(posterior_mean_frames %>% filter(full_name == "Roger Federer", model == "Multi-Norm_bin_games"), 
       aes(x=month, y=posterior_mean, color=skill_type)) +
  geom_line(linewidth=1.0) +
  geom_line(aes(month, lower.025_q), linetype='dashed') +
  geom_line(aes(month, upper.975_q), linetype = 'dashed') +
  ggtitle("Roger Federer") +
  labs(y = "solid: posterior mean; dotted: 95% credible interval", color = "surface") +
  scale_color_manual(labels = c("clay", "grass", "hard"), values = c("red", "forestgreen", "blue"))

ggsave("../manuscript/first_draft/images/federer_combo_1a.png")
## Saving 7 x 5 in image
ggplot(posterior_mean_frames %>% filter(full_name == "Roger Federer", model == "Multi-T_bin_games"), 
       aes(x=month, y=posterior_mean, color=skill_type)) +
  geom_line(linewidth=1.0) +
  geom_line(aes(month, lower.025_q), linetype='dashed') +
  geom_line(aes(month, upper.975_q), linetype = 'dashed') +
  labs(y = "solid: posterior mean; dotted: 95% credible interval", color = "surface") +
  scale_color_manual(labels = c("clay", "grass", "hard"), values = c("red", "forestgreen", "blue")) +
  ggtitle("Roger Federer")

ggsave("../manuscript/first_draft/images/federer_combo_1b.png")
## Saving 7 x 5 in image
ggplot(posterior_mean_frames %>% filter(full_name == "Roger Federer", model == "Multi-Norm_bin_sets"), 
       aes(x=month, y=posterior_mean, color=skill_type)) +
  geom_line(linewidth=1.0) +
  geom_line(aes(month, lower.025_q), linetype='dashed') +
  geom_line(aes(month, upper.975_q), linetype = 'dashed') +
  ggtitle("Roger Federer") +
  labs(y = "solid: posterior mean; dotted: 95% credible interval", color = "surface") +
  scale_color_manual(labels = c("clay", "grass", "hard"), values = c("red", "forestgreen", "blue"))

ggsave("../manuscript/first_draft/images/federer_combo_2a.png")
## Saving 7 x 5 in image
ggplot(posterior_mean_frames %>% filter(full_name == "Roger Federer", model == "Multi-Norm_bin_games"), 
       aes(x=month, y=posterior_mean, color=skill_type)) +
  geom_line(linewidth=1.0) +
  geom_line(aes(month, lower.025_q), linetype='dashed') +
  geom_line(aes(month, upper.975_q), linetype = 'dashed') +
  ggtitle("Roger Federer: Multi-Normal bin games")

ggplot(posterior_mean_frames %>% filter(full_name == "Rafael Nadal", model == "Multi-Norm_bin_games"), 
       aes(x=month, y=posterior_mean, color=skill_type)) +
  geom_line(linewidth=1.0) +
  geom_line(aes(month, lower.025_q), linetype='dashed') +
  geom_line(aes(month, upper.975_q), linetype = 'dashed') +
  ggtitle("Rafa Nadal: Multi-Norm bin games")

ggplot(posterior_mean_frames %>% filter(full_name == "Andy Roddick", model == "Multi-Norm_bin_games"), 
       aes(x=month, y=posterior_mean, color=skill_type)) +
  geom_line(linewidth=1.0) +
  geom_line(aes(month, lower.025_q), linetype='dashed') +
  geom_line(aes(month, upper.975_q), linetype = 'dashed') +
  ggtitle("Andy Roddick: Multi-Norm bin games")

ggplot(posterior_mean_frames %>% filter(full_name == "Tommy Haas", model == "Multi-Norm_bin_games"), 
       aes(x=month, y=posterior_mean, color=skill_type)) +
  geom_line(linewidth=1.0) +
  geom_line(aes(month, lower.025_q), linetype='dashed') +
  geom_line(aes(month, upper.975_q), linetype = 'dashed') +
  ggtitle("del Potro: Multi-Norm bin games")

ggplot(posterior_mean_frames %>% filter(full_name == "Novak Djokovic", model == "Multi-Norm_bin_games"), 
       aes(x=month, y=posterior_mean, color=skill_type)) +
  geom_line(linewidth=1.0) +
  geom_line(aes(month, lower.025_q), linetype='dashed') +
  geom_line(aes(month, upper.975_q), linetype = 'dashed') +
  ggtitle("Djokovic: Multi-Norm bin games")

# See how width of 95% interval changes
ggplot(posterior_mean_frames %>% filter(full_name == "Andy Roddick", model == "Multi-T_bin_games"), 
       aes(x=month, y=(upper.975_q - lower.025_q), color=skill_type)) +
  geom_line(linewidth=1.0) +
  ggtitle("Andy Roddick: Length of 95% Posterior Interval")

ggplot(posterior_mean_frames %>% filter(full_name == "Rafael Nadal", model == "Multi-T_bin_games"), 
       aes(x=month, y=(upper.975_q - lower.025_q), color=skill_type)) +
  geom_line(linewidth=1.0) +
  ggtitle("Rafael Nadal: Length of 95% Posterior Interval")

We can also acquire and plot accuracies.

# Acquire accuraciees
multi_t_bin_games_accs = rbind(read.csv("./multi_t_models_fixed_n_months/multi_t_games_test_acc.csv"),
                               read.csv("./multi_t_models_fixed_n_months/last17_multi_t_games_test_acc.csv"))
multi_t_bin_sets_accs = rbind(read.csv("./multi_t_models_fixed_n_months/multi_t_sets_test_acc.csv"),
                               read.csv("./multi_t_models_fixed_n_months/last17_multi_t_sets_test_acc.csv"))
multi_t_negbin_sets_accs = rbind(read.csv("./multi_t_models_fixed_n_months/multi_t_negbin_sets_test_acc.csv"),
                               read.csv("./multi_t_models_fixed_n_months/last17_multi_t_negbin_sets_test_acc.csv"))

multi_norm_bin_games_accs = rbind(read.csv("./multi_normal_models_fixed_n_months/multi_normal_games_test_acc.csv"),
                                  read.csv("./multi_normal_models_fixed_n_months/last23_multi_normal_games_test_acc.csv"))
multi_norm_bin_sets_accs = rbind(read.csv("./multi_normal_models_fixed_n_months/multi_normal_sets_test_acc.csv"),
                                  read.csv("./multi_normal_models_fixed_n_months/last23_multi_normal_sets_test_acc.csv"))
multi_norm_negbin_sets_accs = rbind(read.csv("./multi_normal_models_fixed_n_months/multi_normal_negbin_sets_test_acc.csv"),
                                  read.csv("./multi_normal_models_fixed_n_months/last23_multi_normal_negbin_sets_test_acc.csv"))

acc_df = data.frame(model = c("Multi-T_bin_games", "Multi-T_bin_sets", "Multi-T_negbin_sets", 
                              "Multi-Normal_bin_games", "Multi-Normal_bin_sets", "Multi-Normal_negbin_sets", "Glicko-2"),
                    average_test_acc = c(mean(multi_t_bin_games_accs$x), mean(multi_t_bin_sets_accs$x), mean(multi_t_negbin_sets_accs$x),
                                         mean(multi_norm_bin_games_accs$x), mean(multi_norm_bin_sets_accs$x), mean(multi_norm_negbin_sets_accs$x), 
                                         mean(glicko_accs)))
acc_df %>%
  arrange(desc(average_test_acc))
##                      model average_test_acc
## 1   Multi-Normal_bin_games        0.6925806
## 2        Multi-T_bin_games        0.6897862
## 3 Multi-Normal_negbin_sets        0.6849412
## 4      Multi-T_negbin_sets        0.6844775
## 5    Multi-Normal_bin_sets        0.6830084
## 6         Multi-T_bin_sets        0.6821852
## 7                 Glicko-2        0.6773777
# OR JUST USE THE ODDS DATA
acc_df = test_out_odds %>%
  group_by(model) %>%
  summarize(acc = mean(pp_p1_match_win_prob > 0.5), n = n())
acc_df = rbind(acc_df, c("Best_odds", mean(one_set_test$winner_implied_prob_best_odds > 0.5), nrow(one_set_test)))
acc_df = rbind(acc_df, c("Average_odds", mean(one_set_test$winner_implied_prob_avg_odds > 0.5), nrow(one_set_test)))
acc_df = rbind(acc_df, c("ATP Rankings", mean(one_set_test_matches$winner_rank < one_set_test_matches$loser_rank), nrow(one_set_test)))
acc_df %>%
  arrange(desc(acc))
## # A tibble: 10 × 3
##    model                  acc               n    
##    <chr>                  <chr>             <chr>
##  1 Best_odds              0.704636319001192 14257
##  2 Average_odds           0.704496037034439 14257
##  3 Multi-Norm_bin_games   0.684646138738865 14257
##  4 Multi-T_bin_games      0.684014869888476 14257
##  5 Multi-Norm_bin_sets    0.681910640387178 14257
##  6 Multi-T_bin_sets       0.680998807603283 14257
##  7 Multi-Norm_negbin_sets 0.679736269902504 14257
##  8 Multi-T_negbin_sets    0.679245283018868 14257
##  9 Glicko-2               0.671880479764326 14257
## 10 ATP Rankings           0.667181033878095 14257

We can also acquire train times to show the complexity of the model

# Acquire train times
multi_t_bin_games_train_times = as.vector(rbind(do.call(rbind, readRDS("./multi_t_models_fixed_n_months/multi_t_games_train_times.RData")),
                                                do.call(rbind, readRDS("./multi_t_models_fixed_n_months/last17_multi_t_games_train_times.RData"))))
multi_t_bin_sets_train_times = as.vector(rbind(do.call(rbind, readRDS("./multi_t_models_fixed_n_months/multi_t_sets_train_times.RData")),
                                               do.call(rbind, readRDS("./multi_t_models_fixed_n_months/last17_multi_t_sets_train_times.RData"))))
multi_t_negbin_sets_train_times = as.vector(rbind(do.call(rbind, readRDS("./multi_t_models_fixed_n_months/multi_t_negbin_sets_train_times.RData")),
                                                  do.call(rbind, readRDS("./multi_t_models_fixed_n_months/last17_multi_t_negbin_sets_train_times.RData"))))

multi_norm_bin_games_train_times = as.vector(rbind(do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/multi_normal_games_train_times.RData")),
                                                   do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/last23_multi_normal_games_train_times.RData"))))
multi_norm_bin_sets_train_times = as.vector(rbind(do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/multi_normal_sets_train_times.RData")),
                                                  do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/last23_multi_normal_sets_train_times.RData"))))
multi_norm_negbin_sets_train_times = as.vector(rbind(do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/multi_normal_negbin_sets_train_times.RData")),
                                                     do.call(rbind, readRDS("./multi_normal_models_fixed_n_months/last23_multi_normal_negbin_sets_train_times.RData"))))

train_time_df = data.frame(model = rep(c("Multi-T_bin_games", "Multi-T_bin_sets", "Multi-T_negbin_sets", 
                              "Multi-Norm_bin_games", "Multi-Norm_bin_sets", "Multi-Norm_negbin_sets"), each = 92),
                           train_time = c(multi_t_bin_games_train_times, multi_t_bin_sets_train_times, multi_t_negbin_sets_train_times,
                                          multi_norm_bin_games_train_times, multi_norm_bin_sets_train_times, multi_norm_negbin_sets_train_times),
                           month = rep(1:92, 6))

# Plot them
ggplot(train_time_df, aes(month, train_time, color = model)) +
  geom_line() +
  scale_color_manual(labels = model.labs, values = c("purple", "navyblue", "red", "hotpink", "darkgreen", "orange")) +
  labs(title = "Model train times", x = "month", y = "train time (s)")

ggsave("../manuscript/first_draft/images/model_train_times.png")
## Saving 7 x 5 in image

Let’s make some posterior mean tables…

# Only rate players with 5 matches played in last year
match_data_365 = atp_match_dat %>% 
  mutate(tourney_date = as.Date(tourney_date), days_passed_since_tourney = -(tourney_date - as.Date('2017-11-01'))) %>% 
  filter(days_passed_since_tourney <= 365)
n_matches_last_year = match_data_365 %>%
  pivot_longer(., cols=c(winner_id, loser_id), names_to = "result", values_to = "player_id") %>%
  group_by(player_id) %>%
  summarize(n = n())
players_to_rate =  n_matches_last_year %>%
  filter(n >= 5) %>%
  pull(player_id)

# Grab top 10 at end of training
top10 = wide_posterior_mean_frames %>%
  filter(month == max(wide_posterior_mean_frames$month),
         model == "Multi-T_bin_games",
         player_id %in% players_to_rate) %>%
  arrange(desc(posterior_mean_hard_skill)) %>%
  select(player_id, full_name, posterior_mean_hard_skill, posterior_mean_clay_skill, posterior_mean_grass_skill) %>% head(10)

top10
## # A tibble: 10 × 5
## # Groups:   player_id, full_name [10]
##    player_id full_name             posterior_mean_hard_skill posterior…¹ poste…²
##    <chr>     <chr>                                     <dbl>       <dbl>   <dbl>
##  1 104925    Novak Djokovic                            0.708       0.692   0.596
##  2 103819    Roger Federer                             0.624       0.538   0.562
##  3 104918    Andy Murray                               0.570       0.514   0.553
##  4 104745    Rafael Nadal                              0.545       0.852   0.412
##  5 105223    Juan Martin del Potro                     0.436       0.515   0.393
##  6 104607    Tomas Berdych                             0.392       0.387   0.351
##  7 103970    David Ferrer                              0.383       0.528   0.312
##  8 104542    Jo-Wilfried Tsonga                        0.360       0.351   0.353
##  9 104527    Stan Wawrinka                             0.337       0.415   0.270
## 10 105227    Marin Cilic                               0.337       0.333   0.315
## # … with abbreviated variable names ¹​posterior_mean_clay_skill,
## #   ²​posterior_mean_grass_skill
# Get their rankings
rankings %>% filter(ranking_date == '2017-11-06') %>% arrange(rank) %>% filter(player %in% top10$player_id)
##    ranking_date rank player points
## 1    2017-11-06    1 104745  10645
## 2    2017-11-06    2 103819   9005
## 3    2017-11-06    5 105227   3805
## 4    2017-11-06    7 104527   3150
## 5    2017-11-06   11 105223   2595
## 6    2017-11-06   12 104925   2585
## 7    2017-11-06   15 104542   2320
## 8    2017-11-06   16 104918   2290
## 9    2017-11-06   19 104607   2095
## 10   2017-11-06   36 103970   1290
#Get top 10 clay players for each model
posterior_mean_frames %>%
  filter(skill_type == "clay_skill", month == "2017-11-01", player_id %in% players_to_rate) %>%
  arrange(model, desc(posterior_mean)) %>%
  group_by(model) %>%
  mutate(rank = rank(-posterior_mean)) %>%
  filter(rank <= 10)
## # A tibble: 60 × 11
## # Groups:   model [6]
##    player_id full_n…¹ skill…² poste…³ poste…⁴ lower…⁵ upper…⁶ poste…⁷ month     
##    <chr>     <chr>    <chr>     <dbl>   <dbl>   <dbl>   <dbl>   <dbl> <date>    
##  1 104745    Rafael … clay_s…   0.859  0.0352   0.792   0.929   0.859 2017-11-01
##  2 104925    Novak D… clay_s…   0.719  0.0399   0.645   0.798   0.720 2017-11-01
##  3 103970    David F… clay_s…   0.590  0.0329   0.527   0.655   0.590 2017-11-01
##  4 105223    Juan Ma… clay_s…   0.556  0.0533   0.452   0.661   0.555 2017-11-01
##  5 103819    Roger F… clay_s…   0.543  0.0378   0.471   0.616   0.543 2017-11-01
##  6 104918    Andy Mu… clay_s…   0.502  0.0421   0.418   0.584   0.501 2017-11-01
##  7 105453    Kei Nis… clay_s…   0.419  0.0515   0.314   0.519   0.419 2017-11-01
##  8 104527    Stan Wa… clay_s…   0.411  0.0342   0.342   0.479   0.411 2017-11-01
##  9 104607    Tomas B… clay_s…   0.403  0.0385   0.328   0.480   0.403 2017-11-01
## 10 104542    Jo-Wilf… clay_s…   0.378  0.0415   0.295   0.458   0.377 2017-11-01
## # … with 50 more rows, 2 more variables: model <chr>, rank <dbl>, and
## #   abbreviated variable names ¹​full_name, ²​skill_type, ³​posterior_mean,
## #   ⁴​posterior_sd, ⁵​lower.025_q, ⁶​upper.975_q, ⁷​posterior_median
# Plot distribution of posterior means for 3 models
ggplot(wide_posterior_mean_frames %>% filter(month == "2017-11-01", model == "Multi-T_bin_games" | model == "Multi-Norm_bin_games" | model == "Multi-T_bin_sets"), aes(posterior_mean_hard_skill, fill = model)) +
  geom_density(alpha=0.4) +
  xlim(-2, 2) +
  ggtitle("Hard court posterior mean distributions") +
  labs(x = 'posterior mean') +
  scale_fill_manual(labels = c("1.(a)", "1.(b)", "2.(a)"), values = c("red", "green", "blue"))
## Warning: Removed 2 rows containing non-finite values (`stat_density()`).

ggsave("../manuscript/first_draft/images/posterior_mean_distn_by_model.png")
## Saving 7 x 5 in image
## Warning: Removed 2 rows containing non-finite values (`stat_density()`).
overall_skills_by_surface = readRDS("./multi_normal_models_fixed_n_months/multi_normal_games_overall_skills_by_surface.RData")

# Get Nadal posterior for 1.(a)
ggplot(overall_skills_by_surface %>% filter(full_name == "Rafael Nadal")) +
  geom_density(aes(x=value, fill = skill_type), alpha = 0.5) + 
  ggtitle("Rafael Nadal Marginal Posteriors") +
  scale_fill_manual(values = c("red", "green", "blue"), labels = c("clay", "grass", "hard")) +
  labs(x = 'skill', fill = 'surface')

ggsave("../manuscript/first_draft/images/nadal_marginal_posteriors.png")
## Saving 7 x 5 in image

Other parameters

R-hat

multi_t_bin_games_skill_summaries = rbind(readRDS("./multi_t_models_fixed_n_months/multi_t_games_skill_summaries.RData"),
                                               readRDS("./multi_t_models_fixed_n_months/last17_multi_t_games_skill_summaries.RData")) %>% last()
## Warning in rbind(readRDS("./multi_t_models_fixed_n_months/
## multi_t_games_skill_summaries.RData"), : number of columns of result is not a
## multiple of vector length (arg 2)
hist(multi_t_bin_games_skill_summaries$rhat)

multi_t_bin_games_skill_summaries %>%
  filter(grepl("beta", variable))
## # A tibble: 1 × 10
##   variable    mean  median      sd     mad      q5     q95  rhat ess_b…¹ ess_t…²
##   <chr>      <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl> <dbl>   <dbl>   <dbl>
## 1 beta     -0.0493 -0.0492 0.00658 0.00662 -0.0601 -0.0387  1.00   3354.   1627.
## # … with abbreviated variable names ¹​ess_bulk, ²​ess_tail
multi_t_bin_games_skill_summaries %>%
  filter(grepl("nu", variable))
## # A tibble: 1 × 10
##   variable  mean median    sd   mad    q5   q95  rhat ess_bulk ess_tail
##   <chr>    <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>    <dbl>    <dbl>
## 1 nu        11.5   9.94  6.16  3.84  5.44  23.2  1.01     684.    1167.
multi_t_bin_games_skill_summaries %>%
  filter(grepl("Sigma", variable))
## # A tibble: 9 × 10
##   variable       mean   median      sd      mad       q5       q95  rhat ess_b…¹
##   <chr>         <dbl>    <dbl>   <dbl>    <dbl>    <dbl>     <dbl> <dbl>   <dbl>
## 1 Sigma[1,1]  0.0253   0.0251  0.00367 0.00358   0.0197   0.0316    1.01   879. 
## 2 Sigma[2,1] -0.00390 -0.00386 0.00183 0.00182  -0.00703 -0.00103   1.00   708. 
## 3 Sigma[3,1] -0.00129 -0.00128 0.00122 0.00120  -0.00323  0.000692  1.02   328. 
## 4 Sigma[1,2] -0.00390 -0.00386 0.00183 0.00182  -0.00703 -0.00103   1.00   708. 
## 5 Sigma[2,2]  0.0147   0.0145  0.00260 0.00255   0.0107   0.0191    1.01   594. 
## 6 Sigma[3,2] -0.00380 -0.00378 0.00113 0.00108  -0.00573 -0.00207   1.03   211. 
## 7 Sigma[1,3] -0.00129 -0.00128 0.00122 0.00120  -0.00323  0.000692  1.02   328. 
## 8 Sigma[2,3] -0.00380 -0.00378 0.00113 0.00108  -0.00573 -0.00207   1.03   211. 
## 9 Sigma[3,3]  0.00283  0.00270 0.00106 0.000999  0.00136  0.00474   1.09    41.4
## # … with 1 more variable: ess_tail <dbl>, and abbreviated variable name
## #   ¹​ess_bulk
#hist(do.call(rbind, multi_norm_sets_skill_summaries)$rhat)
multi_norm_bin_games_skill_summaries = rbind(readRDS("./multi_normal_models_fixed_n_months/multi_normal_games_skill_summaries.RData"),
                                               readRDS("./multi_normal_models_fixed_n_months/last23_multi_normal_games_skill_summaries.RData")) %>% last()
hist(multi_norm_bin_games_skill_summaries$rhat)

multi_norm_bin_games_skill_summaries %>%
  filter(grepl("beta", variable))
## # A tibble: 1 × 10
##   variable    mean  median      sd     mad      q5     q95  rhat ess_b…¹ ess_t…²
##   <chr>      <dbl>   <dbl>   <dbl>   <dbl>   <dbl>   <dbl> <dbl>   <dbl>   <dbl>
## 1 beta     -0.0494 -0.0494 0.00695 0.00694 -0.0609 -0.0380  1.00   3029.   1588.
## # … with abbreviated variable names ¹​ess_bulk, ²​ess_tail
multi_norm_bin_games_skill_summaries %>%
  filter(grepl("nu", variable))
## # A tibble: 0 × 10
## # … with 10 variables: variable <chr>, mean <dbl>, median <dbl>, sd <dbl>,
## #   mad <dbl>, q5 <dbl>, q95 <dbl>, rhat <dbl>, ess_bulk <dbl>, ess_tail <dbl>
multi_norm_bin_games_skill_summaries %>%
  filter(grepl("Sigma", variable))
## # A tibble: 9 × 10
##   variable       mean   median      sd     mad       q5       q95  rhat ess_bulk
##   <chr>         <dbl>    <dbl>   <dbl>   <dbl>    <dbl>     <dbl> <dbl>    <dbl>
## 1 Sigma[1,1]  0.0336   0.0334  0.00351 0.00357  0.0279   0.0395    1.00   1271. 
## 2 Sigma[2,1] -0.00451 -0.00441 0.00219 0.00215 -0.00830 -0.00112   1.00   1013. 
## 3 Sigma[3,1] -0.00201 -0.00205 0.00166 0.00168 -0.00477  0.000750  1.02    395. 
## 4 Sigma[1,2] -0.00451 -0.00441 0.00219 0.00215 -0.00830 -0.00112   1.00   1013. 
## 5 Sigma[2,2]  0.0181   0.0179  0.00280 0.00271  0.0137   0.0232    1.00    712. 
## 6 Sigma[3,2] -0.00426 -0.00420 0.00146 0.00140 -0.00677 -0.00196   1.01    252. 
## 7 Sigma[1,3] -0.00201 -0.00205 0.00166 0.00168 -0.00477  0.000750  1.02    395. 
## 8 Sigma[2,3] -0.00426 -0.00420 0.00146 0.00140 -0.00677 -0.00196   1.01    252. 
## 9 Sigma[3,3]  0.00403  0.00387 0.00134 0.00133  0.00216  0.00639   1.08     47.9
## # … with 1 more variable: ess_tail <dbl>